THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


IN  MEMORY  OF 

Professor 

George    D.  Loooderback 
1874-1957 


Logic 
Inductive  and  Deductive 


BY  WILLIAM  MINTO,  M.A. 

HON.    LL.D.,    ST.   ANDREWS 
LATE  PROFESSOR  OF  LOGIC  IN  THE  UNIVERSITY  OF  ABERDEEN 


WITH  A  FEW  DIAGRAMS 


NEW  YORK 
CHARLES     SCRIBNER'S     SONS 

153-157  FIFTH  AVENUE 
1894 


GIVT 


PREFACE. 

IN  this  little  treatise  two  things  are  attempted 
that  at  first  might  appear  incompatible.  One 
of  them  is  to  put  the  study  of  logical  formulas 
on  a  historical  basis.  Strangely  enough,  the 
scientific  evolution  of  logical  forms,  is  a  bit  of 
history  that  still  awaits  the  zeal  and  genius  of 
some  great  scholar.  I  have  neither  ambition 
nor  qualification  for  such  a  magnum  opus,  and 
my  life  is  already  more  than  half  spent ;  but  the 
gap  in  evolutionary  research  is  so  obvious  that 
doubtless  some  younger  man  is  now  at  work  in 
the  field  unknown  to  me.  All  that  I  can  hope  to- 
do  is  to  act  as  a  humble  pioneer  according  to 
my  imperfect  lights.  Even  the  little  I  have  done 
represents  work  begun  more  than  twenty  years 
ago,  and  continuously  pursued  for  the  last  twelve 
years  during  a  considerable  portion  of  my  time. 

The  other  aim,  which  might  at  first  appear 
inconsistent  with  this,  is  to  increase  the  power 
of  Logic  as  a  practical  discipline.  The  main 
purpose  of  this  practical  science,  or  scientific 
art,  is  conceived  to  be  the  organisation  of  reason 
against  error,  and  error  in  its  various  kinds  is 
made  the  basis  of  the  division  of  the  subject.  To 
carry  out  this  practical  aim  along  with  the  histori- 
cal one  is  not  hopeless,  because  throughout  its 

(T) 
125 


vi  Preface. 

long  history  Logic  has  been  a  practical  science ; 
and,  as  I  have  tried  to  show  at  some  length  in 
introductory  chapters,  has  concerned  itself  at 
different  periods  with  the  risks  of  error  peculiar 
to  each. 

To  enumerate  the  various  books,  ancient  and 
modern,  to  which  I  have  been  indebted,  would  be 
a  vain  parade.  Where  I  have  consciously  adopted 
any  distinctive  recent  contribution  to  the  long  line 
of  tradition,  I  have  made  particular  acknowledg- 
ment. My  greatest  obligation  is  to  my  old  pro- 
fessor, Alexander  Bain,  to  whom  I  owe  my  first 
interest  in  the  subject,  and  more  details  than  I 
can  possibly  separate  from  the  general  body  of  my 
knowledge. 

W.  M. 

ABERDEEN,  January,  1893. 


SINCE  these  sentences  were  written,  the  author  of 
this  book  has  died ;  and  Professor  Minto's  Logic 
is  his  last  contribution  to  the  literature  of  his 
country.  It  embodies  a  large  part  of  his  teaching 
in  the  philosophical  class-room  of  his  University, 
and  doubtless  reflects  the  spirit  of  the  whole  of  it. 

Scottish  Philosophy  has  lost  in  him  one  of  its 
typical  representatives,  and  the  University  of  the 
North  one  of  its  most  stimulating  teachers.  There 
have  been  few  more  distinguished  men  than 
William  Minto  in  the  professoriate  of  Aberdeen ; 
and  the  memory  of  what  he  was,  of  his  wide  and 
varied  learning,  his  brilliant  conversation,  his 
urbanity,  and  his  rare  power  of  sympathy  with 
men  with  whose  opinions  he  did  not  agree,  will 
remain  a  possession  to  many  who  mourn  his  loss. 

It  will  be  something  if  this  little  book  keeps  his 
memory  alive,  both  amongst  the  students  who 
owed  so  much  to  him,  and  in  the  large  circle  of 
friends  who  used  to  feel  the  charm  of  his 
personality. 

WILLIAM  KNIGHT. 


CONTENTS. 

INTRODUCTION. 
I. 

PACK 

The  Origin  and  Scope  of  Logic,   -        -        -         -        -        -         i 

II. 

Logic   as  a   Preventive   of  Error   or   Fallacy — The    Inner 

Sophist, 17 

III. 
The  Axioms  of  Dialectic  and  of  Syllogism,  zg 

BOOK  I. 

THE  LOGIC  OF  CONSISTENCY— SYLLOGISM  AND 
DEFINITION. 

PART  I. 
THE  ELEMENTS  OF  PROPOSITIONS. 

CHAPTER  I. 

General  Names  and  Allied  Distinctions,  43 

CHAPTER  II. 

The  Syllogistic  Analysis  of  Propositions  into  Terms,    (i) 
The  Bare  Analytic  Forms.     (2)  The  Practice  of  Syllo- 
gistic Analysis.     (3)  Some  Technical  Difficulties,  -         -       62 
(ix) 


x  Contents. 

PART  II. 

DEFINITION. 
CHAPTER  I. 

PAGE 

(i)  Imperfect  Understanding  of  Words.  (2)  Verification  of 
the  Meaning — Dialectic.  (3)  Fixation  of  the  Meaning 
— Division  or  Classification,  Definition,  Naming,  82 

CHAPTER  II. 
The  Five  Predicables — Verbal  and  Real  Predication,  -  -  105 

CHAPTER  III. 
Aristotle's  Categories, -  112 

CHAPTER  IV. 
The  Controversy  about  Universals — Difficulties  concerning 

the  Relation  of  General  Names  to  Thought  and  to  Reality,     120 

PART  III. 

THE  INTERPRETATION  OF  PROPOSITIONS. 

CHAPTER  I. 
Theories  of  Predication — Theories  of  Judgment,  -  -  -  131 

CHAPTER  II. 
The  "  Opposition  "  of  Propositions — The  Interpretation  of 

"  No,"  -         - 139 

CHAPTER  III. 

The  Implication  of  Propositions — Immediate  Formal  Infe- 
rence— Eduction,  --------  146 

CHAPTER  IV. 
The  Counter-Implication  of  Propositions,  -  156 

PART  IV. 

THE  INTERDEPENDENCE  OF  PROPOSITIONS. 

CHAPTER  I. 
The  Syllogism, 167 


Contents.  xi 

CHAPTER  II. 

PAGE 

The  Figures  and  Moods  of  the  Syllogism,  (i)  The  First 
Figure.  (2)  The  Minor  Figures  and  their  Reduction  to 
the  First.  (3)  Sorites, i?3 

CHAPTER  III. 
The  Demonstration  of  the  Syllogistic  Moods — The  Canons 

of  the  Syllogism, 185 

CHAPTER  IV. 
The  Analysis  of  Arguments  into  Syllogistic  Forms,      -        -     196 

CHAPTER  V. 
Enthymemes,        -         -         - 205 

CHAPTER  VI. 
The  Utility  of  the  Syllogism, 209 

CHAPTER  VII. 
Conditional  Arguments — Hypothetical  Syllogism,  Disjunctive 

Syllogism  and  Dilemma. 215 

CHAPTER  VIII. 
Fallacies    in    Deductive   Argument — Petitio   Principii    and 

Ignoratio  Elenchi, 226 

CHAPTER  IX. 
Formal  or  Aristotelian    Induction — Inductive  Argument — 

The  Inductive  Syllogism, -     235 

BOOK  II. 

INDUCTIVE  LOGIC,  OR  THE  LOGIC  OF  SCIENCE. 

Introduction, 243 

CHAPTER  I. 
The  Data  of  Experience  as  Grounds  of  Inference  or  Rational 

Belief,    -         -        -        -        .---"•--        .        .        .     273 

CHAPTER  II. 

Ascertainment  of  Simple  Facts  in  their  Order — Personal 
Observation — Hearsay  Evidence — Method  of  Testing 
Traditional  Evidence, 285 


xii  Contents. 

CHAPTER  III. 

PAGE 

Ascertainment  of  Facts  of  Causation,  (i)  Post  Hoc  Ergo 
Propter  Hoc.  '(2)  Meaning  of  Cause — Methods  of  Ob- 
servation— Mill's  Experimental  Methods,  -  -  -  295 

CHAPTER  IV. 

Methods  of  Observation — Single  Difference,  (i)  The  Prin- 
ciple of  Single  Difference.  (2)  Application  of  the 
Principle,  -  308 

CHAPTER  V. 

Methods  of  Observation — Elimination — Single  Agreement, 
(i)  The  Principle  of  Elimination.  (2)  The  Principle  of 
Single  Agreement.  (3)  Mill's  "  Joint  Method  of  Agree- 
ment and  Difference," 318 

CHAPTER  VI. 
Methods  of  Observation — Minor  Methods,     (i)  Concomitant 

Variations.     (2)  Single  Residue, 329 

CHAPTER  VII. 

The  Method  of  Explanation,  (i)  The  Four  Stages  of  Orderly 
Procedure.  (2)  Obstacles  to  Explanation — Plurality  of 
Causes  and  Intermixture  of  Effects.  (3)  The  Proof  of  a 
Hypothesis, -  334 

CHAPTER  VIII. 

Supplementary  Methods  of  Investigation,  (i)  The  Main- 
tenance of  Averages— Supplement  to  the  Method  of 
Difference.  (2)  The  Presumption  from  Extra-Casual 
Coincidence,  351 

CHAPTER  IX. 

Probable   Inference   to   Particulars — The   Measurement    of 

Probability, 362 

CHAPTER  X. 
Inference  from  Analogy,       -  367 


INTRODUCTION. 


I.— THE  ORIGIN  AND  SCOPE  OF  LOGIC. 

THE  question  has  sometimes  been  asked,  Where  should 
we  begin  in  Logic  ?  Particularly  within  the  present 
century  has  this  difficulty  been  felt,  when  the  study 
of  Logic  has  been  revived  and  made  intricate  by  the 
different  purposes  of  its  cultivators. 

Where  did  the  founder  of  Logic  begin  ?  Where  did 
Aristotle  begin  ?  This  seems  to  be  the  simplest  way 
of  settling  where  we  should  begin,  for  the  system 
shaped  by  Aristotle  is  still  the  trunk  of  the  tree, 
though  there  have  been  so  many  offshoots  from  the 
old  stump  and  so  many  parasitic  plants  have  wound 
themselves  round  it  that  Logic  is  now  almost  as 
tangled  a  growth  as  the  Yews  of  Borrowdale — 

An  intertwisted  mass  of  fibres  serpentine 
Upcoiling  and  inveterately  convolved. 

It  used  to  be  said  that  Logic  had  remained  for  two 
thousand  years  precisely  as  Aristotle  left  it.  It  was 
an  example  of  a  science  or  art  perfected  at  one  stroke 
by  the  genius  of  its  first  inventor.  The  bewildered 
student  must  often  wish  that  this  were  so  :  it  is  only 
superficially  true.  Much  of  Aristotle's  nomenclature 
and  his  central  formulas  have  been  retained,  but  they 


2  Introduction. 

have  been  very  variously  supplemented  and  interpreted 
to  very  different  purposes — often  to  no  purpose  at  all. 

The  Cambridge  mathematician's  boast  about  his 
new  theorem — "  The  best  of  it  all  is  that  it  can 
never  by  any  possibility  be  made  of  the  slightest  use 
to  anybody  for  anything" — might  be  made  with  truth 
about  many  of  the  later  developments  of  Logic.  We 
may  say  the  same,  indeed,  about  the  later  develop- 
ments of  any  subject  that  has  been  a  playground  for 
generation  after  generation  of  acute  intellects,  happy  in 
their  own  disinterested  exercise.  Educational  subjects 
— subjects  appropriated  for  the  general  schooling  of 
young  minds — are  particularly  apt  to  be  developed 
out  of  the  lines  of  their  original  intention.  So  many 
influences  conspire  to  pervert  the  original  aim.  The 
convenience  of  the  teacher,  the  convenience  of  the 
learner,  the  love  of  novelty,  the  love  of  symmetry, 
the  love  of  subtlety  ;  easy-going  indolence  on  the  one 
hand  and  intellectual  restlessness  on  the  other — all 
these  motives  act  from  within  on  traditional  matter 
without  regard  to  any  external  purpose  whatever. 
Thus  in  Logic  difficulties  have  been  glossed  over  and 
simplified  for  the  dull  understanding,  while  acute  minds 
have  revelled  in  variations  and  new  and  ingenious 
manipulations  of  the  old  formulae,  and  in  multiplication 
and  more  exact  and  symmetrical  definition  of  the  old 
distinctions. 

To  trace  the  evolution  of  the  forms  and  theories  of 
Logic  under  these  various  influences  during  its  periods 
of  active  development  is  a  task  more  easily  conceived 
than  executed,  and  one  far  above  the  ambition  of  an 
introductory  treatise.  But  it  is  well  that  even  he  who 
writes  for  beginners  should  recognise  that  the  forms 
now  commonly  used  have  been  evolved  out  of  a 


The  Origin  and  Scope  of  Logic.  3 

simpler  tradition.  Without  entering  into  the  details 
of  the  process,  it  is  possible  to  indicate  its  main  stages, 
and  thus  furnish  a  clue  out  of  the  modern  labyrinthine 
confusion  of  purposes. 

How  did  the  Aristotelian  Logic  originate  ?  Its 
central  feature  is  the  syllogistic  forms.  In  what 
circumstances  did  Aristotle  invent  these  ?  For  what 
purpose  ?  What  use  did  he  contemplate  for  them  ? 
In  rightly  understanding  this,  we  shall  understand 
the  original  scope  or  province  of  Logic,  and  thus  be 
in  a  position  to  understand  more  clearly  how  it  has 
been  modified,  contracted,  expanded,  and  supple- 
mented. 

Logic  has  always  made  high  claims  as  the  scientia 
scientiarum^  the  science  of  sciences.  The  builders  of 
this  Tower  of  Babel  are  threatened  in  these  latter  days 
with  confusion  of  tongues.  We  may  escape  this 
danger  if  we  can  recover  the  designs  of  the  founder, 
and  of  the  master-builders  who  succeeded  him. 

Aristotle's  Logic  has  been  so  long  before  the  world 
in  abstract  isolation  that  we  can  hardly  believe  that  its 
form  was  in  any  way  determined  by  local  accident.  A 
horror  as  of  sacrilege  is  excited  by  the  bare  suggestion 
that  the  author  of  this  grand  and  venerable  work, 
one  of  the  most  august  monuments  of  transcendent 
intellect,  was  in  his  day  and  generation  only  a  pre- 
eminent tutor  or  schoolmaster,  and  that  his  logical 
writings  were  designed  for  the  accomplishment  of  his 
pupils  in  a  special  art  in  which  every '  intellectually 
ambitious  young  Athenian  of  the  period  aspired  to 
excel.  Yet  such  is  the  plain  fact,  baldly  stated. 
Aristotle's  Logic  in  its  primary  aim  was  as  practical 
as  a  treatise  on  Navigation,  or  "  Cavendish  on 
Whist".  The  latter  is  the  more  exact  of  the  two 


4  Introduction. 

comparisons.  It  was  in  effect  in  its  various  parts  a 
series  of  handbooks  for  a  temporarily  fashionable  intel- 
lectual game,  a  peculiar  mode  of  disputation  or  dialectic,1 
the  game  of  Question  and  Answer,  the  game  so  fully 
illustrated  in  the  Dialogues  of  Plato,  the  game  identi- 
fied with  the  name  of  Socrates. 

We  may  lay  stress,  if  we  like,  on  the  intellectuality 
of  the  game,  and  the  high  topics  on  which  it  was 
exercised.  It  was  a  game  that  could  flourish  only 
among  a  peculiarly  intellectual  people  ;  a  people  less 
acute  would  find  little  sport  in  it.  The  Athenians 
still  take  a  singular  delight  in  disputation.  You 

1  We  know  for  certain — and  it  is  one  of  the  evidences  of  the 
importance  attached  to  this  trivial-looking  pastime — that  two  of 
the  great  teacher's  logical  treatises,  the  Topics  and  the  Sophistical 
Refutations,  were  written  especially  for  the  guidance  of  Ques- 
tioners and  Respondents.  The  one  instructs  the  disputant  how  to 
qualify  himself  methodically  for  discussion  before  an  ordinary 
audience,  when  the  admissions  extracted  from  the  respondent  are 
matters  of  common  belief,  the  questioner's  skill  being  directed  to 
make  it  appear  that  the  respondent's  position  is  inconsistent  with 
these.  The  other  is  a  systematic  exposure  of  sophistical  tricks, 
mostly  verbal  quibbles,  whereby  a  delusive  appearance  of  victory 
in  debate  may  be  obtained.  But  in  the  concluding  chapter  of  the 
Elenchi,  where  Aristotle  claims  not  only  that  his  method  is 
superior  to  the  empirical  methods  of  rival  teachers,  but  that 
it  is  entirely  original,  it  is  the  Syllogism  upon  which  he  lays 
stress  as  his  peculiar  and  chief  invention.  The  Syllogism,  the 
pure  forms  of  which  are  expounded  in  his  Prior  Analytics,  is  really 
the  centre  of  Aristotle's  logical  system,  whether  the  propositions 
to  which  it  is  applied  are  matters  of  scientific  truth  as  in  the  Pos- 
terior Analytics,  or  matters  of  common  opinion  as  in  the  Topics. 
The  treatise  on  Interpretation,  i.e.,  the  interpretation  of  the 
Respondent's  "  Yes"  and  "  No,"  is  preliminary  to  the  Syllogism, 
the  reasoning  of  the  admissions  together.  Even  in  the  half- 
grammatical  half-logical  treatise  on  the  Categories,  the  author 
always  keeps  an  eye  on  the  Syllogistic  analysis. 


The  Origin  and  Scope  of  Logic.  5 

cannot  visit  Athens  without  being  struck  by  it.  You 
may  still  see  groups  formed  round  two  protagonists 
in  the  cafes  or  the  squares,  or  among  the  ruins  of 
the  Acropolis,  in  a  way  to  remind  you  of  Socrates 
and  his  friends.  They  do  not  argue  as  Gil  Bias  and 
his  Hibernians  did  with  heat  and  temper,  ending 
in  blows.  They  argue  for  the  pure  love  of  arguing, 
the  audience  sitting  or  standing  by  to  see  fair  play 
with  the  keenest  enjoyment  of  intellectual  thrust 
and  parry.  No  other  people  could  argue  like  the 
Greeks  without  coming  to  blows.  It  is  one  of  their 
characteristics  now,  and  so  it  was  in  old  times  two 
thousand  years  ago.  And  about  a  century  before 
Aristotle  reached  manhood,  they  had  invented  this 
peculiarly  difficult  and  trying  species  of  disputative 
pastime,  in  which  we  find  the  genesis  of  Aristotle's 
logical  treatises. 

To  get  a  proper  idea  of  this  debate  by  Question  and 
Answer,  which  we  may  call  Socratic  disputation  after 
its  most  renowned  master,  one  must  read  some  of  the 
dialogues  of  Plato.  I  will  indicate  merely  the  skeleton 
of  the  game,  to  show  how  happily  it  lent  itself  to 
Aristotle's  analysis  of  arguments  and  propositions. 

A  thesis  or  proposition  is  put  up  for  debate,  e.g.,  that 
knowledge  is  nothing  else  than  sensible  perception,1  that 
it  is  a  greater  evil  to  do  wrong  than  to  suffer  wrong,2 
that  the  love  of  gain  is  not  reprehensible.3  There  are 
two  disputants,  but  they  do  not  speak  on  the  question 
by  turns,  so  many  minutes  being  allowed  to  each  as 
in  a  modern  encounter  of  wits.  One  of  the  two,  who 
may  be  called  the  Questioner,  is  limited  to  asking 

1  Theastetus,  151  E.  2  Gorgias,  473  D. 

3  Hipparchus,  225  A. 


6  Introduction. 

questions,  the  other,  the  Respondent,  is  limited  to 
answering.  Further,  the  Respondent  can  answer  only 
"  Yes  "  or  "  No,"  with  perhaps  a  little  explanation  : 
on  his  side  the  Questioner  must  ask  only  questions 
that  admit  of  the  simple  answer  "Yes"  or  "No". 
The  Questioner's  business  is  to  extract  from  the 
Respondent  admissions  involving  the  opposite  of  what 
he  has  undertaken  to  maintain.  The  Questioner  tries 
in  short  to  make  him  contradict  himself.  Only  a 
very  stupid  Respondent  would  do  this  at  once  :  the 
Questioner  plies  him  with  general  principles,  analogies, 
plain  cases;  leads  him  on  from  admission  to  admission, 
and  then  putting  the  admissions  together  convicts  him 
out  of  his  own  mouth  of  inconsistency.1 

Now  mark  precisely  where  Aristotle  struck  in  with 
his  invention  of  the  Syllogism,  the  invention  on  which 
he  prided  himself  as  specially  his  own,  and  the  forms 
of  which  have  clung  to  Logic  ever  since,  even  in  the 
usage  of  those  who  deride  Aristotle's  Moods  and  Figures 
as  antiquated  superstitions.  Suppose  yourself  the 
Questioner,  where  did  he  profess  to  help  you  with  his 
mechanism  ?  In  effect,  as  the  word  Syllogism  indicates, 
it  was  when  you  had  obtained  a  number  of  admissions, 

1  In  its  leading  and  primary  use,  this  was  a  mode  of  debate,  a 
duel  of  wits,  in  which  two  men  engaged  before  an  audience.  But 
the  same  form  could  be  used,  and  was  used,  notably  by  Socrates, 
not  in  an  eristic  spirit  but  as  a  means  of  awakening  people  to  the 
consequences  of  certain  admissions  or  first  principles,  and  thus 
making  vague  knowledge  explicit  and  clear.  The  mind  being 
detained  on  proposition  after  proposition  as  assent  was  given  to 
it,  dialectic  was  a  valuable  instrument  of  instruction  and  exposition. 
But  whatever  the  purpose  of  the  exercise,  controversial  triumph, 
or  solid  grounding  in  first  principles — "the  evolution  of  in-dwelling 
conceptions  " — the  central  interest  lay  in  the  syllogising  or  reasoning 
together  of  the  separately  assumed  or  admitted  propositions. 


The  Origin  and  Scope  of  Logic.  7 

and  wished  to  reason  them  together,  to  demonstrate 
how  they  bore  upon  the  thesis  in  dispute,  how  they 
hung  together,  how  they  necessarily  involved  what 
you  were  contending  for.  And  the  essence  of  his 
mechanism  was  the  reduction  of  the  admitted  proposi- 
tions to  common  terms,  and  to  certain  types  or  forms 
which  are  manifestly  equivalent  or  inter-dependent. 
Aristotle  advised  his  pupils  also  in  the  tactics  of  the 
game,  but  his  grand  invention  was  the  form  or  type  of 
admissions  that  you  should  strive  to  obtain,  and  the 
effective  manipulation  of  them  when  you  had  got 
them. 

An  example  will  show  the  nature  of  this  help,  and 
what  it  was  worth.  To  bring  the  thing  nearer  home, 
let  us,  instead  of  an  example  from  Plato,  whose  topics 
often  seem  artificial  to  us  now,  take  a  thesis  from  last 
century,  a  paradox  still  arguable,  Mandeville's  famous 
— some  would  say  infamous — paradox  that  Private 
Vices  are  Public  Benefits.  Undertake  to  maintain  this, 
and  you  will  have  no  difficulty  in  getting  a  respondent 
prepared  to  maintain  the  negative.  The  plain  men, 
such  as  Socrates  cross-questioned,  would  have  declared 
at  once  that  a  vice  is  a  vice,  and  can  never  do  any  good 
to  anybody.  Your  Respondent  denies  your  proposi- 
tion simply :  he  upholds  that  private  vices  never  are 
public  benefits,  and  defies  you  to  extract  from  him  any 
admission  inconsistent  with  this.  Your  task  then  is  to 
lure  him  somehow  into  admitting  that  in  some  cases 
what  is  vicious  in  the  individual  may  be  of  service  to 
the  State.  This  is  enough  :  you  are  not  concerned  to 
establish  that  this  holds  of  all  private  vices.  A  single 
instance  to  the  contrary  is  enough  to  break  down  his 
universal  negative.  You  cannot,  of  course,  expect 
him  to  make  the  necessary  admission  in  direct  terms  : 


8  Introduction. 

you  must  go  round  about.  You  know,  perhaps,  that 
he  has  confidence  in  Bishop  Butler  as  a  moralist.  You 
try  him  with  the  saying :  "  To  aim  at  public  and 
private  good  are  so  far  from  being  inconsistent  that 
they  mutually  promote  each  other".  Does  he  admit 
this? 

Perhaps  he  wants  some  little  explanation  or  exempli- 
fication to  enable  him  to  grasp  your  meaning.  This 
was  within  the  rules  of  the  game.  You  put  cases  to 
him,  asking  for  his  "  Yes  "  or  "  No  "  to  each.  Suppose 
a  man  goes  into  Parliament,  not  out  of  any  zeal  for 
the  public  good,  but  in  pure  vainglory,  or  to  serve  his 
private  ends,  is  it  possible  for  him  to  render  the  State 
good  service  ?  Or  suppose  a  milk-seller  takes  great 
pains  to  keep  his  milk  pure,  not  because  he  cares  for 
the  public  health,  but  because  it  pays,  is  this  a  benefit 
to  the  public  ? 

Let  these  questions  be  answered  in  the  affirmative, 
putting  you  in  possession  of  the  admission  that  some 
actions  undertaken  for  private  ends  are  of  public 
advantage,  what  must  you  extract  besides  to  make  good 
your  position  as  against  the  Respondent  ?  To  see 
clearly  at  this  stage  what  now  is  required,  though  you 
have  to  reach  it  circuitously,  masking  your  approach 
under  difference  of  language,  would  clearly  be  an 
advantage.  This  was  the  advantage  that  Aristotle's 
method  offered  to  supply.  A  disputant  familiar  with 
his  analysis  would  foresee  at  once  that  if  he  could  get 
the  Respondent  to  admit  that  all  actions  undertaken 
for  private  ends  are  vicious,  the  victory  was  his,  while 
nothing  short  of  this  would  serve. 

Here  my  reader  may  interject  that  he  could  have 
seen  this  without  any  help  from  Aristotle,  and  that 
anybody  may  see  it  without  knowing  that  what  he  has 


The  Origin  and  Scope  of  Logic.  9 

to  do  is,  in  Aristotelian  language,  to  construct  a  syllo- 
gism in  Bokardo.  I  pass  this  over.  I  am  not  con- 
cerned at  this  point  to  defend  the  utility  of  Aristotle's 
method.  All  that  I  want  is  to  illustrate  the  kind  of 
use  that  it  was  intended  for.  Perhaps  if  Aristotle  had 
not  habituated  men's  minds  to  his  analysis,  we  should 
none  of  us  have  been  able  to  discern  coherence  and 
detect  incoherence  as  quickly  and  clearly  as  we  do  now. 
But  to  return  to  our  example.  As  Aristotle's  pupil, 
you  would  have  seen  at  the  stage  we  are  speaking  of 
that  the  establishment  of  your  thesis  must  turn  upon 
the  definition  of  virtue  and  vice.  You  must  proceed, 
therefore,  to  cross-examine  your  Respondent  about 
this.  You  are  not  allowed  to  ask  him  what  he  means 
by  virtue,  or  what  he  means  by  vice.  In  accordance 
with  the  rules  of  the  dialectic,  it  is  your  business  to 
propound  definitions,  and  demand  his  Yes  or  No  to 
them.  You  ask  him,  say,  whether  he  agrees  with 
Shaftesbury's  definition  of  a  virtuous  action  as  an 
action  undertaken  purely  for  the  good  of  others.  If 
he  assents,  it  follows  that  an  action  undertaken  with 
any  suspicion  of  a  self-interested  motive  cannot  be 
numbered  among  the  virtues.  If  he  agrees,  further, 
that  every  action  must  be  either  vicious  or  virtuous, 
you  have  admissions  sufficient  to  prove  your  original 
thesis.  All  that  you  have  now  to  do  to  make  your 
triumph  manifest,  is  to  display  the  admissions  you 
have  obtained  in  common  terms. 

Some  actions  done  with  a  self-interested  motive  are  public 

benefits. 
All  actions  done  with  a  self-interested  motive  are  private 

vices. 

From  these  premisses  it  follows  irresistibly  that 
Some  private  vices  are  public  benefits. 


io  Introduction. 

This  illustration  may  serve  to  show  the  kind  of 
disputation  for  which  Aristotle's  logic  was  designed, 
and  thus  to  make  clear  its  primary  uses  and  its 
limitations. 

To  realise  its  uses,  and  judge  whether  there  is 
anything  analogous  to  them  in  modern  needs,  con- 
ceive the  chief  things  that  it  behoved  Questioner 
and  Respondent  in  this  game  to  know.  All  that  a 
proposition  necessarily  implies ;  all  that  two  proposi- 
tions put  together  imply ;  on  what  conditions  and 
to  what  extent  one  admission  is  inconsistent  with 
another ;  when  one  admission  necessarily  involves 
another  ;  when  two  necessarily  involve  a  third.  And 
to  these  ends  it  was  obviously  necessary  to  have  an 
exact  understanding  of  the  terms  used,  so  as  to  avoid 
the  snares  of  ambiguous  language. 

That  a  Syllogistic  or  Logic  of  Consistency  should 
emerge  out  of  Yes -and -No  Dialectic  was  natural. 
Things  in  this  world  come  when  they  are  wanted : 
inventions  are  made  on  the  spur  of  necessity.  It  was 
above  all  necessary  in  this  kind  of  debate  to  avoid 
contradicting  yourself :  to  maintain  your  consistency. 
A  clever  interrogator  spread  out  proposition  after  pro- 
position before  you  and  invited  your  assent,  choosing 
forms  of  words  likely  to  catch  your  prejudices  and  lure 
you  into  self-contradiction.  An  organon,  instrument, 
or  discipline  calculated  to  protect  you  as  Respondent 
and  guide  you  as  Questioner  by  making  clear  what  an 
admission  led  to,  was  urgently  called  for,  and  when 
the  game  had  been  in  high  fashion  for  more  than  a 
century  Aristotle's  genius  devised  what  was  wanted, 
meeting  at  the  same  time,  no  doubt,  collateral  needs 
that  had  arisen  from  the  application  of  Dialectic  to 
various  kinds  of  subject-matter. 


The  Origin  and  Scope  of  Logic.  1 1 

The  thoroughness  of  Aristotle's  system  was  doubt- 
less due  partly  to  the  searching  character  of  the 
dialectic  in  which  it  had  its  birth.  No  other  mode  of 
disputation  makes  such  demands  upon  the  disputant's 
intellectual  agility  and  precision,  or  is  so  well  adapted 
to  lay  bare  the  skeleton  of  an  argument. 

The  uses  of  Aristotle's  logical  treatises  remained 
when  the  fashion  that  had  called  them  forth  had 
passed.1  Clear  and  consistent  thinking,  a  mastery  of 
the  perplexities  and  ambiguities  of  language,  power  to 
detect  identity  of  meaning  under  difference  of  expres- 
sion, a  ready  apprehension  of  all  that  a  proposition 
implies,  all  that  may  be  educed  or  deduced  from  it — 
whatever  helps  to  these  ends  must  be  of  perpetual  use. 
"  To  purge  the  understanding  of  those  errors  which 
lie  in  the  confusion  and  perplexities  of  an  inconsequent 
thinking,"  is  a  modern  description  of  the  main  scope 
of  Logic.2  It  is  a  good  description  of  the  branch  of 
Logic  that  keeps  closest  to  the  Aristotelian  tradition. 

1  Like  every  other  fashion,  Yes-and-No  Dialectic  had  its  period, 
its  rise  and  fall.     The  invention  of  it  is  ascribed  to  Zeno  the 
Eleatic,   the   answering   and   questioning   Zeno,    who   flourished 
about  the  middle  of  the  fifth  century  B.C.     Socrates  (469-399)  was 
in  his  prime  at  the  beginning  of  the  great  Peloponnesian  War 
when   Pericles  died  in  429.     In  that  year  Plato  was  born,  and 
lived  to  347,  "the  olive  groves  of  Academe  "  being  the  established 
centre  of  his  teaching  from  about  386  onwards.     Aristotle  (384- 
322),  who  was  the  tutor  of  Alexander  the  Great,  established  his 
school  at  the  Lyceum  when  Alexander  became  king  in  336  and 
set  out  on  his  career  of  conquest.     That  Yes-and-No  Dialectic  was 
then  a  prominent  exercise,  his  logical  treatises  everywhere  bear 
witness.     The  subsequent  history  of  the  game  is  obscure.     It  is 
probable   that  Aristotle's   thorough   exposition   of  its   legitimate 
arts  and  illegitimate  tricks  helped  to  destroy  its  interest  as  an 
amusement. 

2  Hamilton's  Lectures,  iii.  p.  37. 


12  Introduction. 

The  limitations  as  well  as  the  uses  of  Aristotle's  logic 
may  be  traced  to  the  circumstances  of  its  origin.  Both 
parties  to  the  disputation,  Questioner  and  Respondent 
alike,  were  mainly  concerned  with  the  inter-dependence 
of  the  propositions  put  forward.  Once  the  Respondent 
had  given  his  assent  to  a  question,  he  was  bound  in 
consistency  to  all  that  it  implied.  He  must  take  all 
the  consequences  of  his  admission.  It  might  be  true 
or  it  might  be  false  as  a  matter  of  fact :  all  the  same 
he  was  bound  by  it  :  its  truth  or  falsehood  was 
immaterial  to  his  position  as  a  disputant.  On  the 
other  hand,  the  Questioner  could  not  go  beyond  the 
admissions  of  the  Respondent.  It  has  often  been 
alleged  as  a  defect  in  the  Syllogism  that  the  conclusion 
does  not  go  beyond  the  premisses,  and  ingenious 
attempts  have  been  made  to  show  that  it  is  really  an 
advance  upon  the  premisses.  But  having  regard  to  the 
primary  use  of  the  syllogism,  this  was  no  defect,  but  a 
necessary  character  of  the  relation.  The  Questioner 
could  not  in  fairness  assume  more  than  had  been 
granted  by  implication.  His  advance  could  only  be  an 
argumentative  advance :  if  his  conclusion  contained  a 
grain  more  than  was  contained  in  the  premisses,  it  was 
a  sophistical  trick,  and  the  Respondent  could  draw 
back  and  withhold  his  assent  He  was  bound  in  con- 
sistency to  stand  by  his  admissions ;  he  was  not 
bound  to  go  a  fraction  of  an  inch  beyond  them. 

We  thus  see  how  vain  it  is  to  look  to  the  Aristotelian 
tradition  for  an  organon  of  truth  or  a  criterion  of 
falsehood.  Directly  and  primarily,  at  least,  it  was  not 
so ;  the  circumstances  of  its  origin  gave  it  a  different 
bent.  Indirectly  and  secondarily,  no  doubt,  it  served 
this  purpose,  inasmuch  as  truth  was  the  aim  of  all 
serious  thinkers  who  sought  to  clear  their  minds  and 


The  Origin  and  Scope-  of  Logic.  13 

the  minds  of  others  by  Dialectic.  But  in  actual  debate 
truth  was  represented  merely  by  the  common-sense  of 
the  audience.  A  dialectician  who  gained  a  triumph  by 
outraging  this,  however  cleverly  he  might  outwit  his 
antagonist,  succeeded  only  in  amusing  his  audience, 
and  dialecticians  of  the  graver  sort  aimed  at  more 
serious  uses  and  a  more  respectful  homage,  and  did 
their  best  to  discountenance  merely  eristic  disputation. 
Further,  it  would  be  a  mistake  to  conclude  because 
Aristotle's  Logic,  as  an  instrument  of  Dialectic,  con- 
cerned itself  with  the  syllogism  of  propositions  rather 
than  their  truth,  that  it  was  merely  an  art  of  quibbling. 
On  the  contrary,  it  was  essentially  the  art  of  preventing 
and  exposing  quibbling.  It  had  its  origin  in  quibbling, 
no  doubt,  inasmuch  as  what  we  should  call  verbal 
quibbling  was  of  the  essence  of  Yes-and-No  Dialectic, 
and  the  main  secret  of  its  charm  for  an  intellectual 
and  disputatious  people ;  but  it  came  into  being  as 
a  safeguard  against  quibbling,  not  a  serviceable 
adjunct. 

The  mediaeval  developments  of  Logic  retained  and 
even  exaggerated  the  syllogistic  character  of  the 
original  treatises.  Interrogative  dialectic  had  disap- 
peared in  the  Middle  Ages  whether  as  a  diversion 
or  as  a  discipline  :  but  errors  of  inconsistency  still 
remained  the  errors  against  which  principally  educated 
men  needed  a  safeguard.  Men  had  to  keep  their 
utterances  in  harmony  with  the  dogmas  of  the  Church. 
A  clear  hold  of  the  exact  implications  of  a  proposition, 
whether  singly  or  in  combination  with  other  proposi- 
tions, was  still  an  important  practical  need.  The 
Inductive  Syllogism  was  not  required,  and  its  treatment 
dwindled  to  insignificance  in  mediaeval  text-books,  but 


£4  Introduction. 

the  Deductive  Syllogism  and  the  formal  apparatus 
for  the  definition  of  terms  held  the  field. 

It  was  when  observation  of  Nature  and  its  laws 
became  a  paramount  pursuit  that  the  defects  of 
Syllogistic  Logic  began  to  be  felt.  Errors  against 
which  this  Logic  offered  no  protection  then  called  for 
a  safeguard — especially  the  errors  to  which  men  are 
liable  in  the  investigation  of  cause  and  effect.  "  Bring 
your  thoughts  into  harmony  one  with  another,"  was 
the  demand  of  Aristotle's  age.  "  Bring  your  thoughts 
into  harmony  with  authority,"  was  the  demand  of  the 
Middle  Ages.  "  Bring  them  into  harmony  with  fact," 
was  the  requirement  most  keenly  felt  in  more  recent 
times.  It  is  in  response  to  this  demand  that  what 
is  commonly  but  not  very  happily  known  as  Inductive 
Logic  has  been  formulated. 

In  obedience  to  custom,  I  shall  follow  the  now 
ordinary  division  of  Logic  into  Deductive  and  Induc- 
tive. The  titles  are  misleading  in  many  ways,  but 
they  are  fixed  by  a  weight  of  usage  which  it  would 
be  vain  to  try  to  unsettle.  Both  come  charging  down 
the  stream  of  time  each  with  its  cohort  of  doctrines 
behind  it,  borne  forward  with  irresistible  momentum. 

The  best  way  of  preventing  confusion  now  is  to 
retain  the  established  titles,  recognise  that  the  doctrines 
behind  each  have  a  radically  different  aim  or  end,  and 
supply  the  interpretation  of  this  end  from  history. 
What  they  have  in  common  may  be  described  as  the 
prevention  of  error,  the  organisation  of  reason  against 
error.  I  have  shown  that  owing  to  the  bent  impressed 
upon  it  by  the  circumstances  of  its  origin,  the  errors 
chiefly  safeguarded  by  the  Aristotelian  logic  were  the 
errors  of  inconsistency.  The  other  branch  of  Logic, 
commonly  called  Induction,  was  really  a  separate 


The  Origin  and  Scope  of  Logic.  15 

evolution,  having  its  origin  in  a  different  practical 
need.  The  history  of  this  I  will  trace  separately 
after  we  have  seen  our  way  through  the  Aristotelian 
tradition  and  its  accretions.  The  Experimental 
Methods  are  no  less  manifestly  the  germ,  the  evolu- 
tionary centre  or  starting-point,  of  the  new  Logic 
than  the  Syllogism  is  of  the  old,  and  the  main  errors 
safeguarded  are  errors  of  fact  and  inference  from 
fact. 

At  this  stage  it  will  be  enough  to  indicate  briefly 
the  broad  relations  between  Deductive  Logic  and 
Inductive  Logic. 

Inductive  Logic,  as  we  now  understand  it — the  Logic 
of  Observation  and  Explanation — was  first  formulated 
and  articulated  to  a  System  of  Logic  by  J.  S.  Mill.  It 
was  he  that  added  this  wing  to  the  old  building.  But 
the  need  of  it  was  clearly  expressed  as  early  as  the 
thirteenth  century.  Roger  Bacon,  the  Franciscan  friar 
(1214-1292),  and  not  his  more  illustrious  namesake 
Francis,  Lord  Verulam,  was  the  real  founder  of 
Inductive  Logic.  It  is  remarkable  that  the  same 
century  saw  Syllogistic  Logic  advanced  to  its  most 
complete  development  in  the  system  of  Petrus 
Hispanus,  a  Portuguese  scholar  who  under  the  title 
of  John  XXI.  filled  the  Papal  Chair  for  eight  months 
in  1276-7. 

A  casual  remark  of  Roger  Bacon's  in  the  course  of 
his  advocacy  of  Experimental  Science  in  the  Opus 
Majus  draws  a  clear  line  between  the  two  branches 
of  Logic.  "There  are,"  he  says,  "two  ways  of 
knowing,  by  Argument  and  by  Experience.  Argument 
concludes  a  question,  but  it  does  not  make  us  feel 
certain,  unless  the  truth  be  also  found  in  ex- 
perience." 


1 6  In  Production . 

On  this  basis  the  old  Logic  may  be  clearly  distinguished 
from  the  new,  taking  as  the  general  aim  of  Logic  the 
protection  of  the  mind  against  the  errors  to  which  it 
is  liable  in  the  acquisition  of  knowledge. 

All  knowledge,  broadly  speaking,  comes  either  from 
Authority,  /.<?.,  by  argument  from  accepted  premisses, 
or  from  Experience.  If  it  comes  from  Authority  it 
comes  through  the  medium  of  words  :  if  it  comes  from 
Experience  it  comes  through  the  senses.  In  taking 
in  knowledge  through  words  we  are  liable  to  certain 
errors ;  and  in  taking  in  knowledge  through  the  senses 
we  are  liable  to  certain  errors.  To  protect  against  the 
one  is  the  main  end  of  "  Deductive"  Logic:  to  protect 
against  the  other  is  the  main  end  of  "  Inductive  " 
Logic.  As  a  matter  of  fact  the  pith  of  treatises  on 
Deduction  and  Induction  is  directed  to  those  ends 
respectively,  the  old  meanings  of  Deduction  and 
Induction  as  formal  processes  (to  be  explained  after- 
wards) being  virtually  ignored. 

There  is  thus  no  antagonism  whatever  between  the 
two  branches  of  Logic.  They  are  directed  to  different 
ends.  The  one  is  supplementary  to  the  other.  The 
one  cannot  supersede  the  other. 

Aristotelian  Logic  can  never  become  superfluous  as 
long  as  men  are  apt  to  be  led  astray  by  words.  Its 
ultimate  business  is  to  safeguard  in  the  interpretation 
of  the  tradition  of  language.  The  mere  syllogistic,  the 
bare  forms  of  equivalent  or  consistent  expression,  have 
a  very  limited  utility,  as  we  shall  see.  But  by  cogent 
sequence  syllogism  leads  to  proposition,  and  proposition 
to  term,  and  term  to  a  close  study  of  the  relations 
between  words  and  thoughts  and  things. 


Logic  as  a  Preventive  of  Error  or  Fallacy.        17 

II.— LOGIC  AS  A  PREVENTIVE  OF  ERROR  OR 
FALLACY.-THE  INNER  SOPHIST. 

Why  describe  Logic  as  a  system  of  defence  against 
error  ?  Why  say  that  its  main  end  and  aim  is  the 
organisation  of  reason  against  confusion  and  false- 
hood ?  WThy  not  rather  say,  as  is  now  usual,  that  its 
end  is  the  attainment  of  truth  ?  Does  this  not  come 
to  the  same  thing  ? 

Substantially,  the  meaning  is  the  same,  but  the 
latter  expression  is  more  misleading.  To  speak  of 
Logic  as  a  body  of  rules  for  the  investigation  of  truth 
has  misled  people  into  supposing  that  Logic  claims  to 
be  an  art  of  Discovery,  that  it  claims  to  lay  down  rules 
by  simply  observing  which  investigators  may  infallibly 
arrive  at  new  truths.  Now,  this  does  not  hold  even  of 
the  Logic  of  Induction,  still  less  of  the  older  Logic,  the 
precise  relation  of  which  to  truth  will  become  apparent 
as  we  proceed.  It  is  only  by  keeping  men  from  going 
astray  and  by  disabusing  them  when  they  think  they 
have  reached  their  destination  that  Logic  helps  men 
on  the  road  to  truth.  Truth  often  lies  hid  in  the  centre 
of  a  maze,  and  logical  rules  only  help  the  searcher 
onwards  by  giving  him  warning  when  he  is  on  the 
wrong  track  and  must  try  another.  It  is  the  searcher's 
own  impulse  that  carries  him  forward  :  Logic  does  not 
so  much  beckon  him  on  to  the  right  path  as  beckon 
him  back  from  the  wrong.  In  laying  down  the  condi- 
tions of  correct  interpretation,  of  valid  argument,  of 
trustworthy  evidence,  of  satisfactory  explanation, 
Logic  shows  the  inquirer  how  to  test  and  purge  his 
conclusions,  not  how  to  reach  them. 

To  discuss,  as  is  sometimes  done,  whether  Fallacies 
lie  within  the  proper  sphere  of  Logic,  is  to  obscure  the 


T  8  Introduction. 

real  connexion  between  Fallacies  and  Logic.  It  is  the 
existence  of  Fallacies  that  calls  Logic  into  existence ; 
as  a  practical  science  Logic  is  needed  as  a  protection 
against  Fallacies.  Such  historically  is  its  origin.  We 
may,  if  we  like,  lay  down  an  arbitrary  rule  that  a 
treatise  on  Logic  should  be  content  to  expound  the 
correct  forms  of  interpretation  and  reasoning  and 
should  not  concern  itself  with  the  wrong.  If  we  take 
this  view  we  are  bound  to  pronounce  Fallacies  extra- 
logical.  But  to  do  so  is  simply  to  cripple  the  useful- 
ness of  Logic  as  a  practical  science.  The  manipulation 
of  the  bare  logical  forms,  without  reference  to  fallacious 
departures  from  them,  is  no  better  than  a  nursery 
exercise.  Every  correct  form  in  Logic  is  laid  down  as 
a  safeguard  against  some  erroneous  form  to  which 
men  are  prone,  whether  in  the  interpretation  of  argu- 
ment or  the  interpretation  of  experience,  and  the 
statement  and  illustration  of  the  typical  forms  oi 
wrong  procedure  should  accompany  part  passu  the 
exposition  of  the  right  procedure. 

In  accordance  with  this  principle,  I  shall  deal  with 
special  fallacies,  special  snares  or  pitfalls — misappre- 
hension of  words,  misinterpretation  of  propositions, 
misunderstanding  of  arguments,  misconstruction  oi 
facts,  evidences,  or  signs — each  in  connexion  with  its 
appropriate  safeguard.  This  seems  to  me  the  most 
profitable  method.  But  at  this  stage,  it  may  be  worth 
while,  by  way  of  emphasising  the  need  for  Logic  as  a 
science  of  rational  belief,  to  take  a  survey  of  the  most 
general  tendencies  to  irrational  belief,  the  chief  kinds 
of  illusion  or  bias  that  are  rooted  in  the  human  consti- 
tution. We  shall  then  better  appreciate  the  magnitude 
of  the  task  that  Logic  attempts  in  seeking  to  protect 


Logic  as  n  Preventive  of  Error  or  Fallacy.        19 

reason  against  its  own  fallibility  and  the  pressure  of 
the  various  forces  that  would  usurp  its  place. 

It  is  a  common  notion  that  we  need  Logic  to  pro- 
tect us  against  the  arts  of  the  Sophist,  the  dishonest 
juggler  with  words  and  specious  facts.  But  in  truth 
the  Inner  Sophist,  whose  instruments  are  our  own 
inborn  propensities  to  error,  is  a  much  more  dangerous 
enemy.  For  once  that  we  are  the  victims  of  designing 
Sophists,  we  are  nine  times  the  victims  of  our  own 
irrational  impulses  and  prejudices.  Men  generally 
deceive  themselves  before  they  deceive  others. 

Francis  Bacon  drew  attention  to  these  inner  per- 
verting influences,  these  universal  sources  of  erroneous 
belief,  in  his  De  Augmentis  and  again  in  his  Novum 
Organum,  under  the  designation  of  Idola  (etScoAa), 
deceptive  appearances  of  truth,  illusions.  His  classi- 
fication of  Idola — Idola  Tribus,  illusions  common  to 
all  men,  illusions  of  the  race  ;  Idola  Specus,  personal 
illusions,  illusions  peculiar  to  the  "  den  "  in  which 
each  man  lives ;  Idola  Fori,  illusions  of  conversation, 
vulgar  prejudices  embodied  in  words ;  Idola  Theatri, 
illusions  of  illustrious  doctrine,  illusions  imposed  by 
the  dazzling  authority  of  great  names — is  defective  as 
a  classification  inasmuch  as  the  first  class  includes  all 
the  others,  but  like  all  his  writings  it  is  full  of  sagacious 
remarks  and  happy  examples.  Not  for  the  sake  of 
novelty,  but  because  it  is  well  that  matters  so  important 
should  be  presented  from  more  than  one  point  of  view, 
I  shall  follow  a  division  adapted  from  the  more  scien- 
tific, if  less  picturesque,  arrangement  of  Professor 
Bain,  in  his  chapter  on  the  Fallacious  Tendencies  of 
the  Human  Mind.1 

1  Bain's  Logic,  bk.  vi.  chap.  iii.  Bacon  intended  his  Idola  tc 
bear  the  same  relation  to  his  Novum  Organum  that  Aristotle's 


2  o  In  tr eduction . 

The  illusions  to  which  we  are  all  subject  may  best 
be  classified  according  to  their  origin  in  the  depths  of 
our  nature.  Let  us  try  to  realise  how  illusory  beliefs 
arise. 

What  is  a  belief?  One  of  the  uses  of  Logic  is 
to  set  us  thinking  about  such  simple  terms.  An 
exhaustive  analysis  and  definition  of  belief  is  one 
of  the  most  difficult  of  psychological  problems.  We 
cannot  enter  upon  that :  let  us  be  content  with  a  few 
simple  characters  of  belief. 

First,  then,  belief  is  a  state  of  mind.  Second,  this 
state  of  mind  is  outward-pointing :  it  has  a  reference 
beyond  itself,  a  reference  to  the  order  of  things  outside 
us.  In  believing,  we  hold  that  the  world  as  it  is,  has 
been,  or  will  be,  corresponds  to  our  conceptions  of 
it.  Third,  belief  is  the  guide  of  action  :  it  is  in  accord- 
ance with  what  we  believe  that  we  direct  our  activities. 
If  we  want  to  know  what  a  man  really  believes,  we 
look  at  his  action.  This  at  least  is  the  clue  to  what 
he  believes  at  the  moment.  "  I  cannot,"  a  great 
orator  once  said,  "  read  the  minds  of  men."  This  was 
received  with  ironical  cheers.  "  No,"  he  retorted,  "  but 
I  can  construe  their  acts."  Promoters  of  companies 
are  expected  to  invest  their  own  money  as  a  guarantee 
of  good  faith.  If  a  man  says  he  believes  the  world  is 
coming  to  an  end  in  a  year,  and  takes  a  lease  of  a 
house  for  fifteen  years,  we  conclude  that  his  belief  is 
not  of  the  highest  degree  of  strength. 

Fallacies  or  Sophistical  Tricks  bore  to  the  old  Organum.  But  in 
truth,  as  I  have  already  indicated,  what  Bacon  classifies  is  our 
inbred  tendencies  to  form  idola  or  false  images,  and  it  is  these 
same  tendencies  that  make  us  liable  to  the  fallacies  named  by 
Aristotle.  Some  of  Aristotle's,  as  we  shall  see,  are  fallacies  of 
Induction. 


Logic  as  a  Preventive  of  Error  or  Fallacy.        21 

The  close  connexion  of  belief  with  our  activities, 
enables  us  to  understand  how  illusions,  false  concep- 
tions of  reality,  arise.  The  illusions  of  Feeling  and 
the  illusions  of  Custom  are  well  understood,  but  other 
sources  of  illusion,  which  may  be  designated  Impatient 
Impulse  and  Happy  Exercise,  are  less  generally 
recognised.  An  example  or  two  will  show  what  is 
meant.  We  cannot  understand  the  strength  of  these 
perverting  influences  till  we  realise  them  in  our  own 
case.  We  detect  them  quickly  enough  in  others. 
Seeing  that  in  common  speech  the  word  illusion 
implies  a  degree  of  error  amounting  almost  to  insanity, 
and  the  illusions  we  speak  of  are  such  as  no  man  is 
ever  quite  free  from,  it  is  perhaps  less  startling  to  use 
the  word  bias. 

The  Bias  of  Impatient  Impulse. 

As  a  being  formed  for  action,  not  only  does  healthy 
man  take  a  pleasure  in  action,  physical  and  mental,  for 
its  own  sake,  irrespective  of  consequences,  but  he  is  so 
charged  with  energy  that  he  cannot  be  comfortable 
unless  it  finds  a  free  vent.  In  proportion  to  the  amount 
and  excitability  of  his  energy,  restraint,  obstruction, 
delay  is  irksome,  and  soon  becomes  a  positive  and 
intolerable  pain.  Any  bar  or  impediment  that  gives  us 
pause  is  hateful  even  to  think  of:  the  mere  prospect 
annoys  and  worries. 

Hence  it  arises  that  belief,  a  feeling  of  being  pre- 
pared for  action,  a  conviction  that  the  way  is  clear 
before  us  for  the  free  exercise  of  our  activities,  is  a  very 
powerful  and  exhilarating  feeling,  as  much  a  necessity 
of  happy  existence  as  action  itself.  We  see  this  when 
we  consider  how  depressing  and  uncomfortable  a 


2  2  Introduction . 

condition  is  the  opposite  state  to  belief,  namely,  doubt, 
perplexity,  hesitation,  uncertainty  as  to  our  course. 
And  realising  this,  we  see  how  strong  a  bias  we 
have  in  this  fact  of  our  nature,  this  imperious  inward 
necessity  for  action  ;  how  it  urges  us  to  act  without 
regard  to  consequences,  and  to  jump  at  beliefs  without 
inquiry.  For,  unless  inquiry  itself  is  our  business,  a 
self-sufficient  occupation,  it  means  delay  and  obstruc- 
tion. 

This  ultimate  fact  of  our  nature,  this  natural  inbred 
constitutional  impatience,  explains  more  than  half  of 
the  wrong  beliefs  that  we  form  and  persist  in.  We 
must  have  a  belief  of  some  kind  :  we  cannot  be  happy 
till  we  get  it,  and  we  take  up  with  the  first  that  seems 
to  show  the  way  clear.  It  may  be  right  or  it  may  be 
wrong :  it  is  not,  of  course,  necessarily  always  wrong  : 
but  that,  so  far  as  we  are  concerned,  is  a  matter  of 
accident.  The  pressing  need  for  a  belief  of  some  sort, 
upon  which  our  energies  may  proceed  in  anticipation 
at  least,  will  not  allow  us  to  stop  and  inquire.  Any 
course  that  offers  a  relief  from  doubt  and  hesitation, 
any  conviction  that  lets  the  will  go  free,  is  eagerly 
embraced. 

It  may  be  thought  that  this  can  apply  only  to  beliefs 
concerning  the  consequences  of  our  own  personal 
actions,  affairs  in  which  we  individually  play  a  part. 
It  is  from  them,  no  doubt,  that  our  nature  takes  this 
set :  but  the  habit  once  formed  is  extended  to  all  sorts 
of  matters  in  which  we  have  no  personal  interest.  Tell 
an  ordinary  Englishman,  it  has  been  wittily  said,  that 
it  is  a  question  whether  the  planets  are  inhabited,  and 
he  feels  bound  at  once  to  have  a  confident  opinion  on 
the  point.  The  strength  of  the  conviction  bears  no 
proportion  to  the  amount  of  reason  spent  in  reaching 


Logic  as  a  Preventive  of  Error  or  Fallacy.        23 

it,  unless  it  may  be  said  that  as  a  general  rule  the  less 
a  belief  is  reasoned  the  more  confidently  it  is  held. 

"A  grocer,"  writes  Mr.  Bagehot  in  an  acute  essay 
on  "  The  Emotion  of  Conviction,"  1  "  has  a  full  creed 
as  to  foreign  policy,  a  young  lady  a  complete  theory 
of  the  Sacraments,  as  to  which  neither  has  any  doubt. 
A  girl  in  a  country  parsonage  will  be  sure  that  Paris 
never  can  be  taken,  or  that  Bismarck  is  a  wretch."  An 
attitude  of  philosophic  doubt,  of  suspended  judgment, 
is  repugnant  to  the  natural  man.  Belief  is  an  inde- 
pendent joy  to  him. 

This  bias  works  in  all  men.  While  there  is  life, 
there  is  pressure  from  within  on  belief,  tending  to  push 
reason  aside.  The  force  of  the  pressure,  of  course, 
varies  with  individual  temperament,  age,  and  other 
circumstances.  The  young  are  more  credulous  than 
the  old,  as  having  greater  energy  :  they  are  apt,  as 
Bacon  puts  it,  to  be  "  carried  away  by  the  sanguine 
element  in  their  temperament ".  Shakespeare's  Laertes 
is  a  study  of  the  impulsive  temperament,  boldly  con- 
trasted with  Hamlet,  who  has  more  discourse  of  reason. 
When  Laertes  hears  that  his  father  has  been  killed,  he 
hurries  home,  collects  a  body  of  armed  sympathisers, 
bursts  into  the  presence  of  the  king,  and  threatens  with 
his  vengeance — the  wrong  man.  He  never  pauses  to 
make  inquiry :  like  Hotspur  he  is  "  a  wasp-stung  and 
impatient  fool "  ;  he  must  wreak  his  revenge  on 
somebody,  and  at  once.  Hamlet's  father  also  has 
been  murdered,  but  his  reason  must  be  satisfied  before 
he  proceeds  to  his  revenge,  and  when  doubtful  proof  is 
offered,  he  waits  for  proof  more  relative. 

Bacon's  Idola  Tribus  and  Dr.  Bain's  illustrations  of 

1  Bagehot's  Literary  Studies,  ii.  427. 


24  Introduction. 

incontinent  energy,  are  mostly  examples  of  unreasoning 
intellectual  activity,  hurried  generalisations,  unsound 
and  superficial  analogies,  rash  hypotheses.  Bacon 
quotes  the  case  of  the  sceptic  in  the  temple  of 
Poseidon,  who,  when  shown  the  offerings  of  those 
who  had  made  vows  in  danger  and  been  delivered, 
and  asked  whether  he  did  not  now  acknowledge  the 
power  of  the  god,  replied  :  "  But  where  are  they  who 
made  vows  and  yet  perished  ?  "  This  man  answered 
rightly,  says  Bacon.  In  dreams,  omens,  retributions, 
and  such  like,  we  are  apt  to  remember  when  they 
come  true  and  to  forget  the  cases  when  they  fail. 
If. we  have  seen  but  one  man  of  a  nation,  we  are 
apt  to  conclude  that  all  his  countrymen  are  like  him  ; 
we  cannot  suspend  our  judgment  till  we  have  seen 
more.  Confident  belief,  as  Dr.  Bain  remarks,  is  the 
primitive  attitude  of  the  human  mind :  it  is  only  by 
slow  degrees  that  this  is  corrected  by  experience. 
The  old  adage,  "  Experience  teaches  fools,"  has  a 
meaning  of  its  own,  but  in  one  sense  it  is  the  reverse 
of  the  truth.  The  mark  of  a  fool  is  that  he  is  not 
taught  by  experience,  and  we  are  all  more  or  less 
intractable  pupils,  till  our  energies  begin  to  fail. 

The  Bias  of  Happy  Exercise. 

If  an  occupation  is  pleasant  in  itself,  if  it  fully 
satisfies  our  inner  craving  for  action,  we  are  liable 
to  be  blinded  thereby  to  its  consequences.  Happy 
exercise  is  the  fool's  Paradise.  The  fallacy  lies  not 
in  being  content  with  what  provides  a  field  for  the 
full  activity  of  our  powers  :  to  be  content  in  such  a 
case  may  be  the  height  of  wisdom :  but  the  fallacy 
lies  in  claiming  for  our  occupation  results,  benefits, 


Logic  as  a  Preventive  of  Error  or  Fallacy.        25 

utilities  that  do  not  really  attend  upon  it.  Thus  we 
see  subjects  of  study,  originally  taken  up  for  some 
purpose,  practical,  artistic,  or  religious,  pursued  into 
elaborate  detail  far  beyond  their  original  purpose, 
and  the  highest  value,  intellectual,  spiritual,  moral, 
claimed  for  them  by  their  votaries,  when  in  truth  they 
merely  serve  to  consume  so  much  vacant  energy,  and 
may  be  a  sheer  waste  of  time  that  ought  to  be  other- 
wise employed. 

But  as  I  am  in  danger  of  myself  furnishing  an 
illustration  of  this  bias — it  is  nowhere  more  prevalent 
than  in  philosophy — I  will  pass  to  our  next  head. 

The  Bias  of  the  Feelings. 

This  source  of  illusion  is  much  more  generally 
understood.  The  blinding  and  perverting  influence 
of  passion  on  reason  has  been  a  favourite  theme  with 
moralists  ever  since  man  began  to  moralise,  and  is 
acknowledged  in  many  a  popular  proverb.  "  Love  is 
blind  ;  "  "  The  wish  is  father  to  the  thought ;  "  "  Some 
people's  geese  are  all  swans  ;  "  and  so  forth. 

We  need  not  dwell  upon  the  illustration  of  it.  Fear 
and  Sloth  magnify  dangers  and  difficulties ;  Affection 
can  see  no  imperfection  in  its  object :  in  the  eyes  of 
Jealousy  a  rival  is  a  wretch.  From  the  nature  of  the 
case  we  are  much  more  apt  to  see  examples  in  others 
than  in  ourselves.  If  the  strength  of  this  bias  were 
properly  understood  by  everybody,  the  mistake  would 
not  so  often  be  committed  of  suspecting  bad  faith, 
conscious  hypocrisy,  when  people  are  found  practising 
the  grossest  inconsistencies,  and  shutting  their  eyes 
apparently  in  deliberate  wilfulness  to  facts  held  under 
their  very  noses.  Men  are  inclined  to  ascribe  this 


26  Introduction. 

human  weakness  to  women.  Reasoning  from  feeling 
is  said  to  be  feminine  logic.  But  it  is  a  human 
weakness. 

To  take  one  very  powerful  feeling,  the  feeling  of 
self-love  or  self-interest — this  operates  in  much  more 
subtle  ways  than  most  people  imagine,  in  ways  so 
subtle  that  the  self-deceiver,  however  honest,  would 
fail  to  be  conscious  of  the  influence  if  it  were  pointed 
out  to  him.  When  the  slothful  man  saith,  There  is  a 
lion  in  the  path,  we  can  all  detect  the  bias  to  his 
belief,  and  so  we  can  when  the  slothful  student  says 
that  he  will  work  hard  to-morrow,  or  next  week,  or 
next  month  ;  or  when  the  disappointed  man  shows  an 
exaggerated  sense  of  the  advantages  of  a  successful 
rival  or  of  his  own  disadvantages.  But  self-interest 
works  to  bias  belief  in  much  less  palpable  ways  than 
those.  It  is  this  bias  that  accounts  for  the  difficulty 
that  men  of  antagonistic  interests  have  in  seeing  the 
arguments  or  believing  in  the  honesty  of  their 
opponents.  You  shall  find  conferences  held  between 
capitalists  and  workmen  in  which  the  two  sides,  both 
represented  by  men  incapable  of  consciously  dishonest 
action,  fail  altogether  to  see  the  force  of  each  other's 
arguments,  and  are  mutually  astonished  each  at  the 
other's  blindness. 

The  Bias  of  Custom. 

That  custom,  habits  of  thought  and  practice,  affect 
belief,  is  also  generally  acknowledged,  though  the 
strength  and  wide  reach  of  the  bias  is  seldom  realised. 
Very  simple  cases  of  unreasoning  prejudice  were 
adduced  by  Locke,  who  was  the  first  to  suggest  a 
general  explanation  of  them  in  the  "  Association  of 


Logic  as  a  Preventive  of  Error   or  Fallacy.        2  7 

Ideas"  (Human  Understanding^,  ii.  ch.  xxxiii.).  There 
is,  for  instance,  the  fear  that  overcomes  many  people 
when  alone  in  the  dark.  In  vain  reason  tells  them  that 
there  is  no  real  danger ;  they  have  a  certain  tremor  of 
apprehension  that  they  cannot  get  rid  of,  because 
darkness  is  inseparably  connected  in  their  minds  with 
images  of  horror.  Similarly  we  contract  unreasonable 
dislikes  to  places  where  painful  things  have  happened 
to  us.  Equally  unreasoning,  if  not  unreasonable,  is 
our  attachment  to  customary  doctrines  or  practices, 
and  our  invincible  antipathy  to  those  who  do  not 
observe  them. 

Words  are  very  common  vehicles  for  the  currency 
of  this  kind  of  prejudice,  good  or  bad  meanings  being 
attached  to  them  by  custom.  The  power  of  words  in 
this  way  is  recognised  in  the  proverb:  "  Give  a  dog 
a  bad  name,  and  then  hang  him ".  These  verbal 
prejudices  are  Bacon's  Idola  Fori,  illusions  of  conver- 
sation. Each  of  us  is  brought  up  in  a  certain  sect  or 
party,  and  accustomed  to  respect  or  dishonour  certain 
sectarian  or  party  names,  Whig,  Tory,  Radical, 
Socialist,  Evolutionist,  Broad,  Low,  or  High  Church. 
We  may  meet  a  man  without  knowing  under  what 
label  he  walks  and  be  charmed  with  his  company : 
meet  him  again  when  his  name  is  known,  and  all  is 
changed. 

Such  errors  are  called  Fallacies  of  Association  to 
point  to  the  psychological  explanation.  This  is  that 
by  force  of  association  certain  ideas  are  brought  into 
the  mind,  and  that  once  they  are  there,  we  cannot  help 
giving  them  objective  reality.  For  example,  a  doctor 
comes  to  examine  a  patient,  and  finds  certain 
symptoms.  He  has  lately  seen  or  heard  of  many  cases 
of  influenza,  we  shall  say ;  influenza  is  running  in  his 


2  8  Introduction . 

head.  The  idea  once  suggested  has  all  the  advantage 
of  possession. 

But  why  is  it  that  a  man  cannot  get  rid  of  an  idea  ? 
Why  does  it  force  itself  upon  him  as  a  belief  ?  Associa- 
tion, custom,  explains  how  it  got  there,  but  not  why  it 
persists  in  staying. 

To  explain  this  we  must  call  in  our  first  fallacious 
principle,  the  Impatience  of  Doubt  or  Delay,  the 
imperative  inward  need  for  a  belief  of  some  sort. 

And  this  leads  to  another  remark,  that  though  for 
convenience  of  exposition,  we  separate  these  various 
influences,  they  are  not  separated  in  practice.  They 
may  and  often  do  act  all  together,  the  Inner  Sophist 
concentrating  his  forces. 

Finally,  it  may  be  asked  whether,  seeing  that 
illusions  are  the  offspring  of  such  highly  respectable 
qualities  as  excess  of  energy,  excess  of  feeling,  excess 
of  docility,  it  is  a  good  thing  for  man  to  be  disillu- 
sioned. The  rose-colour  that  lies  over  the  world  for 
youth  is  projected  from  the  abundant  energy  and 
feeling  within  :  disillusion  comes  with  failing  energies, 
when  hope  is  "  unwilling  to  be  fed  ".  Is  it  good  then 
to  be  disillusioned  ?  The  foregoing  exposition  would 
be  egregiously  wrong  if  the  majority  of  mankind  did 
not  resent  the  intrusion  of  Reason  and  its  organising 
lieutenant  Logic.  But  really  there  is  no  danger  that 
this  intrusion  succeeds  to  the  extent  of  paralysing 
action  and  destroying  feeling,  and  uprooting  custom. 
The  utmost  that  Logic  can  do  is  to  modify  the  excess 
of  these  good  qualities  by  setting  forth  the  conditions 
of  rational  belief.  The  student  who  masters  those 
conditions  will  soon  see  the  practical  wisdom  of 
applying  his  knowledge  only  in  cases  where  the 
grounds  of  rational  belief  are  within  his  reach.  To 


The  Axioms  of  Dialectic  and  of  Syllogism.        29 

apply  it  to  the  consequences  of  every  action  would  be 
to  yield  to  that  bias  of  incontinent  activity  which  is, 
perhaps,  our  most  fruitful  source  of  error. 


III.— THE  AXIOMS  OF  DIALECTIC  AND  OF 
SYLLOGISM. 

There  are  certain  principles  known  as  the  Laws  of 
Thought  or  the  Maxims  of  Consistency.  They  are 
variously  expressed,  variously  demonstrated,  and 
variously  interpreted,  but  in  one  form  or  another  they 
are  often  said  to  be  the  foundation  of  all  Logic.  It 
is  even  said  that  all  the  doctrines  of  Deductive  or 
Syllogistic  Logic  may  be  educed  from  them.  Let  us 
take  the  most  abstract  expression  of  them,  and  see 
how  they  originated.  Three  laws  are  commonly 
given,  named  respectively  the  Law  of  Identity,  the 
Law  of  Contradiction  and  the  Law  of  Excluded 
Middle. 

1.  The   Law    of  Identity.      A   is   A.       Socrates    is 
Socrates.     Guilt  is  guilt. 

2.  The  Law    of   Contradiction.      A    is    not    not- A. 
Socrates  is   not    other   than    Socrates.      Guilt  is  not 
other  than   guilt.     Or  A  is  not  at  once  b  and  not-£. 
Socrates  is  not  at  once  good  and  not-good.     Guilt  is 
not  at  once  punishable  and  not-punishable. 

3.  The   Law   of  Excluded  Middle.      Everything   is 
either  A  or  not-A  ;  or,  A  is  either  b  or  not-<£.     A  given 
thing  is  either  Socrates  or  not- Socrates,  either  guilty 
or  not-guilty.     It  must  be  one  or  the  other:  no  middle 
is  possible. 

Why  lay  down  principles  so  obvious,  in  some  inter- 
pretations, and  so  manifestly  sophistical  in  others  ? 
The  bare  forms  of  modern  Logic  have  been  reached 


30  Introduction. 

by  a  process  of  attenuation  from  a  passage  in  Aristotle's 
Metaphysics*  (iii.  3,  4,  1005^  -  1008).  He  is  there 
laying  down  the  first  principle  of  demonstration,  which 
he  takes  to  be  that  "  it  is  impossible  that  the  same 
predicate  can  both  belong,  and  not  belong,  to  the  same 
subject,  at  the  same  time,  and  in  the  same  sense  ".2 
That  Socrates  knows  grammar,  and  does  not  know 
grammar — these  two  propositions  cannot  both  be 
true  at  the  same  time,  and  in  the  same  sense.  Two 
contraries  cannot  exist  together  in  the  same  subject. 
The  double  answer  Yes  and  No  cannot  be  given  to  one 
and  the  same  question  understood  in  the  same  sense. 

But  why  did  Aristotle  consider  it  necessary  to  lay 
down  a  principle  so  obvious  ?  Simply  because  among 
the  subtle  dialecticians  who  preceded  him  the  principle 
had  been  challenged.  The  Platonic  dialogue  Euthy- 
demus  shows  the  farcical  lengths  to  which  such 
quibbling  was  carried.  The  two  brothers  vanquish 
all  opponents,  but  it  is  oy  claiming  that  the  answer 
No  does  not  preclude  the  answer  Yes.  "  Is  not  the 
honourable  honourable,  and  the  base  base  ?  "  asks 
Socrates.  "That  is  as  I  -  please,"  replies  Dionyso- 
dorus.  Socrates  concludes  that  there  is  no  arguing 
with  such  men :  they  repudiate  the  first  principles  of 
dialectic. 

There  were,  however,  more  respectable  practitioners 

1  The  first  statement  of  the  Law  of  Identity  in  the  form  Ens 
est   ens   is   ascribed  by  Hamilton  (Lectures,  iii.  91)   to  Antonius 
Andreas,  a  fourteenth  century  commentator  on  the  Metaphysics. 
But  Andreas  is  merely  expounding  what  Aristotle  sets  forth  in 
iii.  4,   1006  «,  b.     Ens  est  ens  does  not  mean  in  Andreas  what 
A  is  A   means  in   Hamilton. 

2  rb  yap  avrb  a/J.a  U7rap%eii/  re  /cal  /JL)]  vTrapxflv  o-^vvarov  rep  avrtf 
Kxl  Kara  rb  curb,   .   .   .  OUTTJ  8?)  iraffuv  e«rr:   /8e/3cuoTaT7)  rwv 

«.i.  3,  10056,  19-23. 


The  Axoims  of  Dialectic  and  of  Syllogism.         31 

who  canvassed  on  more  plausible  grounds  any  form 
into  which  ultimate  doctrines  about  contraries  and 
contradictions,  truth  and  falsehood,  could  be  put,  and 
therefore  Aristotle  considered  it  necessary  to  put  forth 
an  d  defend  at  elaborate  length  a  statement  of  a  first 
principle  of  demonstration.  "  Contradictions  cannot 
both  be  true  of  the  same  subject  at  the  same  time 
and  in  the  same  sense."  This  is  the  original  form  of 
the  Law  of  Contradiction. 

The  words  "  of  the  same  subject,"  "  at  the  same 
time,"  and  "  in  the  same  sense,"  are  carefully  chosen 
to  guard  against  possible  quibbles.  "  Socrates  knows 
grammar."  By  Socrates  we  must  mean  the  same 
individual  man.  And  even  of  the  same  man  the 
assertion  may  be  true  at  one  time  and  not  at  another. 
There  was  a  time  when  Socrates  did  not  know 
grammar,  though  he  knows  it  now.  And  the  assertion 
may  be  true  in  one  sense  and  not  in  another.  It  may 
be  true  that  Socrates  knows  grammar,  yet  not  that  he 
knows  everything  that  is  to  be  known  about  grammar, 
or  that  he  knows  as  much  as  Aristarchus. 

Aristotle  acknowledges  that  this  first  principle 
cannot  itself  be  demonstrated,  that  is,  deduced  from 
any  other.  If  it  is  denied,  you  can  only  reduce  the 
denier  to  an  absurdity.  And  in  showing  how  to 
proceed  in  so  doing,  he  says  you  must  begin  by 
coming  to  an  agreement  about  the  words  used,  that 
they  signify  the  same  for  one  and  the  other  disputant.1 

1  Hamilton  credits  Andreas  with  maintaining,  "  against  Aris- 
totle," that  "the  principle  of  Identity,  and  not  the  principle  of 
Contradiction,  is  the  one  absolutely  first".  Which  comes  first,  is 
a  scholastic  question  on  which  ingenuity  may  be  exercised.  But 
in  fact  Aristotle  put  the  principle  of  Identity  first  in  the  above 
plain  sense,  and  Andreas  only  expounded  more  formally  what 
Aristotle  had  said. 


32  Introduction. 

No  dialectic  is  possible  without  this  understanding, 
This  first  principle  of  Dialectic  is  the  original  of  the 
Law  of  Identity.  While  any  question  as  to  the 
truth  or  falsehood  of  a  question  is  pending,  from  the 
beginning  to  the  end  of  any  logical  process,  the  words- 
must  continue  to  be  accepted  in  the  same  sense, 
Words  must  have  an  identical  reference  to  things. 

Incidentally  in  discussing  the  Axiom  of  Contradiction 
(a&o}fj.a  TTJ<S  dim^acrews),1  Aristotle  lays  down  what  is  now 
known  as  the  Law  of  Excluded  Middle.  Of  two  con- 
tradictories one  or  other  must  be  true  :  we  must  either 
affirm  or  deny  any  one  thing  of  any  other  :  no  mean 
or  middle  is  possible. 

In  their  origin,  then,  these  so-called  Laws  of  Thought 
were  simply  the  first  principles  of  Dialectic  and 
Demonstration.  Consecutive  argument,  coherent 
ratiocination,  is  impossible  unless  they  are  taken  for 
granted. 

If  we  divorce  or  abstract  them  from  their  original 
application,  and  consider  them  merely  as  laws  of 
thinking  or  of  being,  any  abstract  expression,  or 
illustration,  or  designation  of  them  may  easily  be 
pushed  into  antagonism  with  other  plain  truths  or 
first  principles  equally  rudimentary.  Without  entering 
into  the  perplexing  and  voluminous  discussion  ta 
which  these  laws  have  been  subjected  by  logicians 
within  the  last  hundred  years,  a  little  casuistry  is 
necessary  to  enable  the  student  to  understand  within 
what  limits  they  hold  good. 

Socrates  is  Socrates.     The  name  Socrates  is  a  name 


ev  Kad   evbs  OTIOVV.     Metaph.  iii.  7,  10116,  23-4. 


The  Axioms  of  Dialectic  and  of  Syllogism.        33 

for  something  to  which  you  and  I  refer  when  we 
use  the  name.  Unless  we  have  the  same  reference, 
we  cannot  hold  any  argument  about  the  thing,  or 
make  any  communication  one  to  another  about  it. 

But  if  we  take  Socrates  is  Socrates  to  mean  that,  "  An 
object  of  thought  or  thing  is  identical  with  itself,"  "An 
object  of  thought  or  thing  cannot  be  other  than  itself," 
and  call  this  a  law  of  thought,  we  are  met  at  once  by 
a  difficulty.  Thought,  properly  speaking,  does  not 
begin  till  we  pass  beyond  the  identity  of  an  object 
with  itself.  Thought  begins  only  when  we  recognise 
the  likeness  between  one  object  and  others.  To  keep 
within  the  self-identity  of  the  object  is  to  suspend 
thought.  "  Socrates  was  a  native  of  Attica," 
"  Socrates  was  a  wise  man,"  "  Socrates  was  put  to 
death  as  a  troubler  of  the  commonweal " — whenever 
we  begin  to  think  or  say  anything  about  Socrates,  to 
ascribe  any  attributes  to  him,  we  pass  out  of  his  self- 
identity  into  his  relations  of  likeness  with  other  men, 
into  what  he  has  in  common  with  other  men. 

Hegelians  express  this  plain  truth  with  paradoxical 
point  when  they  say :  "Of  any  definite  existence 
or  thought,  therefore,  it  may  be  said  with  quite 
as  much  truth  that  it  is  not,  as  that  it  ist  its  own 
bare  self".1  Or,  "  A  thing  must  other  itself  in  order 
to  be  itself".  Controversialists  treat  this  as  a  sub- 
version of  the  laws  of  Identity  and  Contradiction. 
But  it  is  only  Hegel's  fun — his  paradoxical  way  of 
putting  the  plain  truth  that  any  object  has  more  in 
common  with  other  objects  than  it  has  peculiar  to 
itself.  Till  we  enter  into  those  aspects  of  agreement 
with  other  objects,  we  cannot  truly  be  said  to  think  at 

1  Prof.  Caird's  Hegel,  p.  138. 
3 


34  Introduction. 

all.  If  we  say  merely  that  a  thing  is  itself,  we  may 
as  well  say  nothing  about  it.  To  lay  down  this  is  not 
to  subvert  the  Law  of  Identity,  but  to  keep  it  from 
being  pushed  to  the  extreme  of  appearing  to  deny  the 
Law  of  Likeness,  which  is  the  foundation  of  all  the 
characters,  attributes,  or  qualities  of  things  in  our 
thoughts. 

That  self-same  objects  are  like  other  self-same 
objects,  is  an  assumption  distinct  from  the  Law  of 
Identity,  and  any  interpretation  of  it  that  excludes 
this  assumption  is  to  be  repudiated.  But  does  not 
the  law  of  Identity  as  well  as  the  law  of  the  likeness 
of  mutually  exclusive  identities  presuppose  that  there 
are  objects  self- same,  like  others,  and  different  from 
others  ?  Certainly  :  this  is  one  of  the  presuppositions 
of  Logic.1  We  assume  that  the  world  of  which  we 
talk  and  reason  is  separated  into  such  objects  in  our 
thoughts.  We  assume  that  such  words  as  Socrates 
represent  individual  objects  with  a  self-same  being  or 
substance;  that  such  words  as  wisdom,  humour,  ugliness, 
running,  sitting,  here,  there,  represent  attributes,  quali- 
ties, characters  or  predicates  of  individuals ;  that 
such  words  as  man  represent  groups  or  classes  of 
individuals. 

Some  logicians  in  expressing  the  Law  of  Identity 
have  their  eye  specially  upon  the  objects  signified 
by  general  names  or  abstract  names,  man,  education? 
"A  concept  is  identical  with  the  sum  of  its  characters," 
or,  "  Classes  are  identical  with  the  sum  of  the  indi- 
viduals composing  them".  The  assumptions  thus 
expressed  in  technical  language  which  will  hereafter 

1  See  Venn,  Empirical  Logic,  1-8. 

2  E.g.,  Hamilton,  lect.  v. ;  Veitch's  Institutes  of  Logic,  chaps, 
xii.,  xiii. 


The  Axioms  of  Dialectic  and  of  Syllogism.        35 

be  explained  are  undoubtedly  assumptions  that  Logic 
makes  :  but  since  they  are  statements  of  the  internal 
constitution  of  some  of  the  identities  that  words  repre- 
sent, to  call  them  the  Law  of  Identity  is  to  depart 
confusingly  from  traditional  usage.1 

That  throughout  any  logical  process  a  word  must 
signify  the  same  object,  is  one  proposition :  that  the 
object  signified  by  a  general  name  is  identical  with 
the  sum  of  the  individuals  to  each  of  whom  it  is 
applicable,  or  with  the  sum  of  the  characters  that 
they  bear  in  common,  is  another  proposition.  Logic 
assumes  both:  Aristotle  assumed  both,:  but  it  is  the 
first  that  is  historically  the  original  of  all  expressions 
of  the  Law  of  Identity  in  modern  text-books. 

Yet  another  expression  of  a  Law  of  Identity  which 
is  really  distinct  from  and  an  addition  to  Aristotle's 
original.  Socrates  was  an  Athenian,  a  philosopher,  an 
ugly  man,  an  acute  dialectician,  etc.  Let  it  be  granted 
that  the  word  Socrates  bears  the  same  signification 
throughout  all  these  and  any  number  more  of  predi- 
cates, we  may  still  ask  :  "  But  what  is  it  that  Socrates 
signifies  ?  "  The  title  Law  of  Identity  is  sometimes 
given 2  to  a  theory  on  this  point.  Socrates  is  Socrates. 
"  An  individual  is  the  identity  running  through  the 
totality  of  its  attributes."  Is  this  not,  it  may  be 

1  The  confusion  probably  arises  in  this  way.  First,  these 
"  laws  "  are  formulated  as  laws  of  thought  that  Logic  assumes. 
Second,  a  notion  arises  that  these  laws  are  the  only  postulates  of 
Logic:  that  all  logical  doctrines  can  be  "evolved"  from  them. 
Third,  when  it  is  felt  that  more  than  the  identical  reference  of 
words  or  the  identity  of  a  thing  with  itself  must  be  assumed  in 
Logic,  the  Law  of  Identity  is  extended  to  cover  this  further 
assumption. 

"E.g.,  Bosanquet's  Logic,  ii.  207. 


3  6  Introduction . 

asked,  to  confuse  thought  and  being,  to  resolve 
Socrates  into  a  string  of  words  ?  No  :  real  existence 
is  one  of  the  admissible  predicates  of  Socrates :  one 
of  the  attributes  under  which  we  conceive  him.  But 
whether  we  accept  or  reject  this  "  Law  of  Identity," 
it  is  an  addition  to  Aristotle's  dialectical  "law  of 
identity "  ;  it  is  a  theory  of  the  metaphysical  nature 
of  the  identity  signified  by  a  Singular  name.  And 
the  same  may  be  said  of  yet  another  theory  of  Identity, 
that,  "  An  individual  is  identical  with  the  totality  of  its 
predicates,"  or  (another  way  of  putting  the  same  theory), 
"  An  individual  is  a  conflux  of  generalities  ". 

To  turn  next  to  the  Laws  of  Contradiction  and 
Excluded  Middle.  These  also  may  be  subjected  to 
Casuistry,  making  clearer  what  they  assert  by  showing 
what  they  do  not  deny. 

They  do  not  deny  that  things  change,  and  that  suc- 
cessive states  of  the  same  thing  may  pass  into  one 
another  by  imperceptible  degrees.  A  thing  may  be 
neither  here  nor  there  :  it  may  be  on  the  passage 
from  here  to  there  :  and,  while  it  is  in  motion,  we 
may  say,  with  equal  truth,  that  it  is  neither  here  nor 
there,  or  that  it  is  both  here  and  there.  Youth  passes 
gradually  into  age,  day  into  night :  a  given  man  or  a 
given  moment  may  be  on  the  borderland  between  the 
two. 

Logic  does  not  deny  the  existence  of  indeterminate 
margins:  it  merely  lays  down  that  for  purposes  of 
clear  communication  and  coherent  reasoning  the  line 
must  be  drawn  somewhere  between  b,  and  not-^. 

A  difference,  however,  must  be  recognised  between 
logical  negation  and  the  negations  of  common  thought 
and  common  speech.  The  latter  are  definite  to  a 


The  Axioms  of  Dialectic  and  of  Syllogism.        37 

degree  with  which  the  mere  Logic  of  Consistency  does 
not  concern  itself.  To  realise  this  is  to  understand 
more  clearly  the  limitations  of  Formal  Logic. 

In  common  speech,  to  deny  a  quality  of  anything  is 
by  implication  to  attribute  to  it  some  other  quality  of 
the  same  kind.  Let  any  man  tell  me  that "  the  streets 
of  such  and  such  a  town  are  not  paved  with  wood,"  I 
at  once  conclude  that  they  are  paved  with  some  other 
material.  It  is  the  legitimate  effect  of  his  negative 
proposition  to  convey  this  impression  to  my  mind.  If, 
proceeding  on  this,  I  go  on  to  ask :  "  Then  they  are 
paved  with  granite  or  asphalt,  or  this  or  that  ?  "  and 
he  turns  round  and  says :  "  I  did  not  say  they  were 
paved  at  all,"  I  should  be  justified  in  accusing  him  of 
a  quibble.  In  ordinary  speech,  to  deny  one  kind  of 
pavement  is  to  assert  pavement  of  some  kind.  Simi- 
larly, to  deny  that  So-and-so  is  not  in  the  Twenty- 
first  Regiment,  is  to  imply  that  he  is  in  another 
regiment,  that  he  is  in  the  army  in  some  regiment. 
To  retort  upon  this  inference  :  "  He  is  not  in  the 
army  at  all,"  is  a  quibble  :  as  much  so  as  it  would  be 
to  retort :  "  There  is  no  such  person  in  existence  ". 

Now  Logic  does  not  take  account  of  this  implication, 
and  nothing  has  contributed  more  to  bring  upon  it  the 
reproach  of  quibbling.  In  Logic,  to  deny  a  quality  is 
simply  to  declare  a  repugnance  between  it  and  the 
subject ;  negation  is  mere  sublation,  taking  away,  and 
implies  nothing  more.  Not-£  is  entirely  indefinite  : 
it  may  cover  anything  except  b. 

Is  Logic  then  really  useless,  or  even  misleading, 
inasmuch  as  it  ignores  the  definite  implication  of 
negatives  in  ordinary  thought  and  speech  ?  In  ignor- 
ing this  implication,  does  Logic  oppose  this  implication 
as  erroneous  ?  Does  Logic  shelter  the  quibbler  who 


38  Introduction. 

trades  upon  it  ?  By  no  means  :  to  jump  to  this  con- 
clusion were  a  misunderstanding.  The  fact  only  is 
that  nothing  beyond  the  logical  Law  of  Contradiction 
needs  to  be  assumed  for  any  of  the  processes  of  Formal 
Logic.  Aristotle  required  to  assume  nothing  more  for 
his  syllogistic  formulae,  and  Logic  has  not  yet  included 
in  its  scope  any  process  that  requires  any  further 
assumption.  "  If  not-<£  represent  everything  except  ^, 
everything  outside  £,  then  that  A  is  b,  and  that  A  is 
not-£,  cannot  both  be  true,  and  one  or  other  of  them 
must  be  true." 

Whether  the  scope  of  Logic  ought  to  be  extended  is 
another  question.  It  seems  to  me  that  the  scope  of 
Logic  may  legitimately  be  extended  so  as  to  take 
account  both  of  the  positive  implication  of  negatives 
and  the  negative  implication  of  positives.  I  therefore 
deal  with  this  subject  in  a  separate  chapter  following 
on  the  ordinary  doctrines  of  Immediate  Inference, 
where  I  try  to  explain  the  simple  Law  of  Thought 
involved.  When  I  say  that  the  extension  is  legitimate, 
I  mean  that  it  may  be  made  without  departing  from 
the  traditional  view  of  Logic  as  a  practical  science, 
conversant  with  the  nature  of  thought  and  its  expression 
only  in  so  far  as  it  can  provide  practical  guidance 
against  erroneous  interpretations  and  inferences.  The 
extension  that  I  propose  is  in  effect  an  attempt  to  bring 
within  the  fold  of  Practical  Logic  some  of  the  results 
of  the  dialectic  of  Hegel  and  his  followers,  such  as  Mr. 
Bradley  and  Mr.  Bosanquet,  Professor  Caird  and  Pro- 
fessor Wallace.1 

The  logical  processes  formulated   by  Aristotle  are 


1  Bradley,  Principles  of  Logic ;  Bosanquet,  Logic  or  The 
Morphology  of  Knowledge  ;  Caird,  Hegel  (in  Blackwood's 
Philosophical  Classics) ;  Wallace,  The  Logic  of  Hegel. 


The  Axioms  of  Dialectic  and  of  Syllogism.        39 

merely  stages  in  the  movement  of  thought  towards 
attaining  definite  conceptions  of  reality.  To  treat 
their  conclusions  as  positions  in  which  thought  may 
dwell  and  rest,  is  an  error,  against  which  Logic  itself 
as  a  practical  science  may  fairly  be  called  upon  to 
guard.  It  may  even  be  conceded  that  the  Aristotelian 
processes  are  artificial  stages,  courses  that  thought 
does  not  take  naturally,  but  into  which  it  has  to  be 
forced  for  a  purpose.  To  concede  this  is  not  to  con- 
cede that  the  Aristotelian  logic  is  useless,  as  long  as 
we  have  reason  on  our  side  in  holding  that  thought  is 
benefited  and  strengthened  against  certain  errors  by 
passing  through  those  artificial  stages. 


BOOK    I. 

THE  LOGIC  OF  CONSISTENCY.     SYLLOGISM  AND 
DEFINITION. 


PART  I. 
THE  ELEMENTS  OF  PROPOSITIONS. 

CHAPTER  I. 

GENERAL  NAMES  AND  ALLIED  DISTINCTIONS. 

To  discipline  us  against  the  errors  we  are  liable  to 
in  receiving  knowledge  through  the  medium  of 
words — such  is  one  of  the  objects  of  Logic,  the 
main  object  of  what  may  be  called  the  Logic  of 
Consistency. 

Strictly  speaking,  we  may  receive  knowledge  about 
things  through  signs  or  single  words,  as  a  nod,  a  wink, 
a  cry,  a  call,  a  command.  But  an  assertory  sentence, 
proposition,  or  predication,  is  the  unit  with  which  Logic 
concerns  itself — a  sentence  in  which  a  subject  is  named 
and  something  is  said  or  predicated  about  it.  Let  a 
man  once  understand  the  errors  incident  to  this  regular 
mode  of  communication,  and  he  may  safely  be  left  to 
protect  himself  against  the  errors  incident  to  more 
rudimentary  modes. 

A  proposition,  whether  long  or  short,  is  a  unit,  but 
it  is  an  analy sable  unit.  And  the  key  to  syllogistic 
(43) 


44  The  Elements  of  Propositions. 

analysis  is  the  General  Name.  Every  proposition, 
every  sentence  in  which  we  convey  knowledge  to 
another,  contains  a  general  name  or  its  equivalent. 
That  is  to  say,  every  proposition  may  be  resolved 
into  a  form  in  which  the  predicate  is  a  general  name. 
A  knowledge  of  the  function  of  this  element  of  speech 
is  the  basis  of  all  logical  discipline.  Therefore,  though 
we  must  always  remember  that  the  proposition  is 
the  real  unit  of  speech,  and  the  general  name 
only  an  analytic  element,  we  take  the  general  name 
and  its  allied  distinctions  in  thought  and  reality 
first. 

How  propositions  are  analysed  for  syllogistic 
purposes  will  be  shown  by-and-by,  but  we  must 
first  explain  various  technical  terms  that  logicians 
have  devised  to  define  the  features  of  this  cardinal 
element.  The  technical  terms  CLASS,  CONCEPT, 
NOTION,  ATTRIBUTE,  EXTENSION  or  DENOTATION, 
INTENSION  or  CONNOTATION,  GENUS,  SPECIES,  DIFFER- 
ENTIA, SINGULAR  NAME,  COLLECTIVE  NAME,  ABSTRACT 
NAME,  all  centre  round  it. 

A  general  name  is  a  name  applicable  to  a  number 
of  different  things  on  the  ground  of  some  likeness 
among  them,  as  man,  ratepayer,  man  of  courage, 
man  who  fought  at  Waterloo. 

From  the  examples  it  will  be  seen  that  a  general 
name  logically  is  not  necessarily  a  single  word.  Any 
word  or  combination  of  words  that  serves  a  certain 
function  is  technically  a  general  name.  The  different 
ways  of  making  in  common  speech  the  equivalent  of 
a  general  name  logically  are  for  the  grammarian  to 
consider. 

In  the  definition  of  a  general  name  attention  is  called 
to  two  distinct  considerations,  the  individual  objects  to 


General  Names  and  Allied  Distinctions.  45 

each  of  which  the  name  is  applicable,  and  the  points  of 
resemblance  among  them,  in  virtue  of  which  they  have 
a  common  name.  For  those  distinctions  there  are 
technical  terms. 

Class  is  the  technical  term  for  the  objects,  different 
yet  agreeing,  to  each  of  which  a  general  name  may  be 
applied. 

The  points  of  resemblance  are  called  the  common 
attributes  of  the  class. 

A  class  may  be  constituted  on  one  attribute  or  on 
several.  Ratepayer,  woman  ratepayer,  unmarried  Woman 
ratepayer:  soldier,  British  soldier,  British  soldier  on 
foreign  service.  Bui  every  individual  to  which  the 
general  name  can  be  applied  must  possess  the  common 
attribute  or  attributes. 

These  common  attributes  are  also  called  the  Notion 
of  the  class,  inasmuch  as  it  is  them  that  the  mind 
notes  or  should  note  when  the  general  name  is  applied. 
Concept  is  a  synonym  perhaps  in  more  common  use 
than  notion  ;  the  rationale  of  this  term  (derived  from 
con  and  capere,  to  take  or  grasp  together)  being  that  it 
is  by  means  of  the  points  of  resemblance  that  the 
individuals  are  grasped  or  held  together  by  the  mind. 
These  common  points  are  the  one  in  the  many,  the 
same  amidst  the  different,  the  identity  signified  by  the 
common  name.  The  name  of  an  attribute  as  thought 
of  by  itself  without  reference  to  any  individual  or  class 
possessing  it,  is  called  an  Abstract  name.  By  con- 
tradistinction, the  name  of  an  individual  or  a  class  is 
Concrete. 

Technical  terms  are  wanted  also  to  express  the 
relation  of  the  individuals  and  the  attributes  to  the 
general  name.  The  individuals  jointly  are  spoken  of 
as  the  Denotation,  or  Extension  or  Scope  of  the 


46  The  Elements  of  Propositions. 

name ;  the  common  attributes  as  its  Connotation, 
Intension,  Comprehension,  or  Ground.  The  whole 
denotation,  etc.,  is  the  class  ;  the  whole  connotation, 
etc.,  is  the  concept.1 


1  It  has  been  somewhat  too  hastily  assumed  on  the  authority 
of  Mansel  (Note  to  Aldrich,  pp.  16,  17)  that  Mill  inverted  the 
scholastic  tradition  in  his  use  of  the  word  Connotative.  Mansel 
puts  his  statement  doubtfully,  and  admits  that  there  was  some 
licence  in  the  use  of  the  word  Connotative,  but  holds  that  in 
Scholastic  Logic  an  adjective  was  said  to  "  signify  primarily  the 
attribute,  and  to  connote  or  signify  secondarily  (irpoa-ff-ri /naive iv)  the 
subject  of  inhesion ".  The  truth  is  that  Mansel's  view  was  a 
theory  of  usage  n  t  a  statement  of  actual  usage,  and  he  had  good 
reason  for  putting  it  doubtfully. 

As  a  matter  of  fact,  the  history  of  the  distinction  follows  the 
simple  type  of  increasing  precision  and  complexity,  and  Mill  was 
in  strict  accord  with  standard  tradition.  By  the  Nominalist 
commentators  on  the  Summulce  of  Petrus  Hispanus  certain  names, 
adjectives  grammatically,  are  called  Connotativa  as  opposed  to 
Absoluta,  simply  because  they  have  a  double  function.  White  is 
connotative  as  signifying  both  a  subject,  such  as  Socrates,  of 
whom  "whiteness"  is  an  attribute,  and  an  attribute  "whiteness": 
the  names  "  Socrates "  and  "whiteness"  are  Absolute,  as  having 
but  a  single  signification.  Occam  himself  speaks  of  the  subject 
as  the  primary  signification,  and  the  attribute  as  the  secondary, 
because  the  answer  to  "What  is  white?"  is  "  Something  informed 
with  whiteness,"  and  the  subject  is  in  the  nominative  case  while 
the  attribute  is  in  an  oblique  case  (Logic,  part  i.  chap.  x.).  Later 
on  we  find  that  Tataretus  (Expositio  in  Summulas,  A.D.  1501), 
while  mentioning  (Tract.  Sept.  De  Appellationibus)  that  it  is  a 
matter  of  dispute  among  Doctores  whether  a  connotative  name 
connotat  the  subject  or  the  attribute,  is  perfectly  explicit  in  his 
own  definition,  "  Terminus  connotativus  est  qui  praeter  illud  pro 
quo  supponit  connotat  aliquid  adjacere  vel  non  adjacere  rei  pro 
qua  supponit"  (Tract.  Sept.  De  Suppositwnibus}.  And  this 
remained  the  standard  usage  as  long  as  the  distinction  remained 
in  logical  text-books.  We  find  it  very  clearly  expressed  by 
Clichtoveus,  a  Nominalist,  quoted  as  an  authority  by  Guthutius 


General  Names  and  Allied  Distinctions.          47 

The  limits  of  a  "  class  "  in  Logic  are  fixed  by  the 
common  attributes.  Any  individual  object  that 

in  his  Gymnasium  Speculativum,  Paris,  1607  (De  Terminorum 
Cognitione,  pp.  78-9).  "  Terminus  absolutus  est,  qui  solum  illud 
pro  quo  in  propositione  supponit,  significat.  Connotativus  autem, 
qui  ultra  idipsum,  aliud  importat."  Thus  man  and  animal  are 
absolute  terms,  which  simply  stand  for  (supponunt  pro)  the  things 
they  signify.  White  is  a  connotative  name,  because  "  it  stands 
for  (supponit  pro)  a  subject  in  which  it  is  an  accident :  and  beyond 
this,  still  signifies  an  accident,  which  is  in  that  subject,  and  is 
expressed  by  an  abstract  name  ".  Only  Clichtoveus  drops  the 
verb  connotat,  perhaps  as  a  disputable  term,  and  says  simply  ultra 
importat. 

So  in  the  Port  Royal  Logic  (1662),  from  which  possibly  Mill 
took  the  distinction :  "  Les  noms  qui  signifient  les  choses  comme 
modifiees,  marquant  premierement  et  directement  la  chose,  quoi- 
que  plus  confusement,  et  indirectement  le  mode,  quoique  plus 
distinctement,  sont  appeles  adjectifs  ou  connotatifs  ;  comme  rond, 
dur,  juste,  prudent"  (part  i.  chap.  ii.). 

What  Mill  did  was  not  to  invert  Scholastic  usage  but  to  revive 
the  distinction,  and  extend  the  word  connotative  to  general  names 
on  the  ground  that  they  also  imported  the  possession  of  attributes. 
The  word  has  been  as  fruitfu  of  meticulous  discussion  as  it  was 
in  the  Renaissance  of  Logic,  though  the  ground  has  changed. 
The  point  of  Mill's  innovation  was,  premising  that  general  names 
are  not  absolute  but  are  applied  in  virtue  of  a  meaning,  to  put 
emphasis  on  this  meaning  as  the  cardinal  consideration.  What 
he  called  the  connotation  had  dropped  out  of  sight  as  not  being 
required  in  the  Syllogistic  Forms.  This  was  as  it  were  the  point 
at  which  he  put  in  his  horn  to  toss  the  prevalent  conception  of 
Logic  as  Syllogistic. 

The  real  drift  of  Mill's  innovation  has  been  obscured  by  the 
fact  that  it  was  introduced  among  the  preliminaries  of  Syllogism, 
whereas  its  real  usefulness  and  significance  belongs  not  to 
Syllogism  in  the  strict  sense  but  to  Definition.  He  added  to 
the  confusion  by  trying  to  devise  forms  of  Syllogism  based  on 
connotation,  and  by  discussing  the  Axiom  of  the  Syllogism  from 
this  point  of  view.  For  syllogistic  purposes,  as  we  shall  see, 
Aristotle's  forms  are  perfect,  and  his  conception  of  the  proposition 


48  The  Elements  of  Propositions. 

possesses  these  is  a  member.  The  statement  of  them 
is  the  Definition. 

To  predicate  a  general  name  of  any  object,  as, 
"This  is  a  cat,"  "This  is  a  very  sad  affair,"  is  to 
refer  that  object  to  a  class,  which  is  equivalent  to 
saying  that  it  has  certain  features  of  resemblance  with 
other  objects,  that  it  reminds  us  of  them  by  its  likeness 
to  them.  Thus  to  say  that  the  predicate  of  every 
proposition  is  a  general  name,  expressed  or  implied,  is 
the  same  as  to  say  that  every  predication  may  be 
taken  as  a  reference  to  a  class. 

Ordinarily  our  notion  or  concept  of  the  common 
features  signified  by  general  names  is  vague  and  hazy. 
The  business  of  Logic  is  to  make  them  clear.  It  is  to 
this  end  that  the  individual  objects  of  the  class  are 


in  extension  the  only  correct  conception.  Whether  the  centre 
of  gravity  in  Consistency  Logic  should  not  be  shifted  back 
from  Syllogism  to  Definition,  the  latter  being  the  true  centre 
of  consistency,  is  another  question.  The  tendency  of  Mill's 
polemic  was  to  make  this  change.  And  possibly  the  secret  of 
the  support  it  has  recently  received  from  Mr.  Bradley  and  Mr. 
Bosanquet  is  that  they,  following  Hegel,  are  moving  in  the 
same  direction. 

In  effect,  Mill's  doctrine  of  Connotation  helped  to  fix  a  con- 
ception of  the  general  name  first  dimly  suggested  by  Aristotle 
when  he  recognised  that  names  of  genera  and  species  signify 
Quality,  in  showing  what  sort  a  thing  is.  Occam  carried  this  a 
step  farther  towards  clear  light  by  including  among  Connotative 
Terms  such  general  names  as  "  monk,"  names  of  classes  that  at 
once  suggest  a  definite  attribute.  The  third  step  was  made  by 
Mill  in  extending  the  term  Connotation  to  such  words  as  "  man," 
"  horse,"  the  Infimce  Species  of  the  Schoolmen,  the  Species  of 
modern  science. 

Whether  connotation  was  the  best  term  to  use  for  this  purpose, 
rather  than  extension,  may  be  questioned :  but  at  least  it  was  in 
the  line  of  tradition  through  Occam. 


General  Names  and  Allied  Distinctions.  49 

summoned  before  the  mind.  In  ordinary  thinking 
there  is  no  definite  array  or  muster  of  objects  :  when 
we  think  of  "dog"  or  "cat,"  "accident,"  "book," 
"beggar,"  "ratepayer,"  we  do  not  stop  to  call  before 
the  mind  a  host  of  representatives  of  the  class,  nor  do 
we  take  precise  account  of  their  common  attributes. 
The  concept  of  "  house  "  is  what  all  houses  have  in 
common.  To  make  this  explicit  would  be  no  easy 
matter,  and  yet  we  are  constantly  referring  objects  to 
the  class  "house".  We  shall  see  presently  that  if 
we  wish  to  make  the  connotation  or  concept  clear  we 
must  run  over  the  denotation  or  class,  that  is  to  say, 
the  objects  to  which  the  general  name  is  applied  in 
common  usage.  Try,  for  example,  to  conceive  clearly 
what  is  meant  by  house,  tree,  dog,  walking-stick. 
You  think  of  individual  objects,  so-called,  and  of  what 
they  have  in  common. 

A  class  may  be  constituted  on  one  property  or  on 
many.  There  are  several  points  common  to  all 
houses,  enclosing  walls,  a  roof,  a  means  of  exit  and 
entrance.  For  the  full  concept  of  the  natural  kinds, 
men,  dogs,  mice,  etc.,  we  should  have  to  go  to  the 
natural  historian. 

Degrees  of  generality.  One  class  is  said  to  be  of 
higher  generality  than  another  when  it  includes  that 
other  and  more.  Thus  animal  includes  man,  dog, 
horse,  etc. ;  man  includes  Aryan,  Semite,  etc. ;  Aryan 
includes  Hindoo,  Teuton,  Celt,  etc. 

The  technical  names  for  higher  and  lower  classes 
are  Genus  and  Species.  These  terms  are  not  fixed  as 
in  Natural  History  to  certain  grades,  but  are  purely 
relative  one  to  another,  and  movable  up  and  down  a 
scale  of  generality.  A  class  may  be  a  species 
relatively  to  one  class,  which  is  above  it,  and  a  genus 

4 


50  The  Elements  of  Propositions. 

relatively  to  one  below  it.  Thus  Aryan  is  a  species 
of  the  genus  man,  Teuton  a  species  of  the  genus 
Aryan. 

In  the  graded  divisions  of  Natural  History  genus 
and  species  are  fixed  names  for  certain  grades.  Thus  : 
Vertebrates  form  a  "  division  "  ;  the  next  subdivision, 
e.g.,  Mammals,  Birds,  Reptiles,  etc.,  is  called  a  "  class"; 
the  next,  e.g..  Rodents,  Carnivora,  Ruminants,  an 
"order";  the  next,  e.g.,  Rats,  Squirrels,  Beavers,  a 
"  genus "  ;  the  next,  e.g.,  Brown  rats,  Mice,  a 
"species". 

Vertebrates  (division). 

i 

i 

Mammals,  Birds,  Reptiles,  etc.  (class). 
Rodents,  Ruminants,  Carnivors,  etc.  (order). 
Rats,  Squirrels,  Beavers,  etc.  (genus). 
Brown  rats,  Mice,  etc.  (species). 

If  we  subdivide  a  large  class  into  smaller  classes, 
and,  again,  subdivide  these  subdivisions,  we  come  at 
last  to  single  objects. 

Men. 


Europeans,  Asiatics,  etc. 


Englishmen,  Frenchmen,  etc. 


John  Doe,  Richard  Roe,  etc. 


General  Names  and  Allied  Distinctions. 


51 


A  table  of  higher  and  lower  classes  arranged  in  order 
has  been  known  from  of  old  as  a  tree  of  division  or 
classification.  The  following  is  Porphyry's  '*  tree  "  : — 

Being 


Corporeal 


Animate 


Sensible 


Rational 


Incorporeal 


Inanimate 


Insensible 


Irrational 


Socrates,  Plato,  and  other  individuals. 


52  The  Elements  of  Propositions. 

The  single  objects  are  called  Individuals,  because 
the  division  cannot  be  carried  farther.  The  highest 
class  is  technically  the  Summum  Genus,  or  Genus 
generalissimum  ;  the  next  highest  class  to  any  species 
is  the  Proximum  Genus ;  the  lowest  group  before  you 
descend  to  individuals  is  the  Infima  Species,  or  Species 
specialissima. 

The  attribute  or  attributes  whereby  a  species  is 
distinguished  from  other  species  of  the  same  genus,  is 
called  its  differentia  or  differentiae.  The  various 
species  of  houses  are  differentiated  by  their  several 
uses,  dwelling-house,  town-house,  ware-house,  public- 
house.  Poetry  is  a  species  of  Fine  Art,  its  differentia 
being  the  use  of  metrical  language  as  its  instrument. 

A  lower  class,  indicated  by  the  name  of  its  higher 
class  qualified  by  adjectives  or  adjective  phrases 
expressing  its  differential  property  or  properties,  is  said 
to  be  described  per  genus  et  differentiam.  Examples  : 
"  Black-bird,"  "  note-book,"  "  clever  man/'  "  man  of 
Kent,"  "  eminent  British  painter  of  marine  subjects  ". 
By  giving  a  combination  of  attributes  common  to  him 
with  nobody  else,  we  may  narrow  down  the  application 
of  a  name  to  an  individual :  "  The  Commander-in- 
Chief  of  the  British  forces  at  the  battle  of  Waterloo  ". 

Other  attributes  of  classes  as  divided  and  defined, 
have  received  technical  names. 

An  attribute  common  to  all  the  individuals  of  a 
class,  found  in  that  class  only,  and  following  from  the 
essential  or  defining  attributes,  though  not  included 
among  them,  is  called  a  Proprium. 

An  attribute  that  belongs  to  some,  but  not  to  all,  or 
that  belongs  to  all,  but  is  not  a  necessary  consequence 
of  the  essential  attributes,  is  called  an  Accident. 

The   clearest    examples    of   Propria    are    found     in 


General  Names  and  Allied  -Distinctions.  53 

mathematical  figures.  Thus,  the  defining  property  of 
an  equilateral  triangle  is  the  equality  of  the  sides  :  the 
equality  of  the  angles  is  a  proprium.  That  the  three 
angles  of  a  triangle  are  together  equal  to  two  right 
angles  is  a  proprium,  true  of  all  triangles,  and  deducible 
from  the  essential  properties  of  a  triangle. 

Outside  Mathematics,  it  is  not  easy  to  find  propria 
that  satisfy  the  three  conditions  of  the  definition.  It 
is  a  useful  exercise  of  the  wits  to  try  for  such.  Edu- 
cability — an  example  of  the  proprium  in  mediaeval 
text-books — is  common  to  men,  and  results  from  man's 
essential  constitution  ;  but  it  is  not  peculiar ;  other 
animals  are  educable.  That  man  cooks  his  food  is 
probably  a  genuine  proprium. 

That  horses  run  wild  in  Thibet :  that  gold  is  found 
in  California :  that  clergymen  wear  white  ties,  are 
examples  of  Accidents.  Learning  is  an  accident  in 
man,  though  educability  is  a  proprium. 

What  is  known  technically  as  an  Inseparable 
Accident,  such  as  the  black  colour  of  the  crow  or  the 
Ethiopian,  is  not  easy  to  distinguish  from  the  Pro- 
prium. It  is  distinguished  only  by  the  third  character, 
deducibility- from  the  essence.1 

1  The  history  of  the  definition  of  the  Proprium  is  an  example  of 
the  tendency  of  distinctions  to  become  more  minute  and  at  the 
same  time  more  purposeless.  Aristotle's  "iSiov  was  an  attribute, 
such  as  the  laugh  of  the  man  or  the  bark  of  the  dog,  common  to 
all  of  a  class  and  peculiar  to  the  class  (quod  convenit  omni  soli  et 
semper}  yet  not  comprised  in  the  definition  of  the  class.  Porphyry 
recognised  three  varieties  of  18ia  besides  this,  four  in  all,  as 
follows : — (i)  an  attribute  peculiar  to  a  species  but  not  possessed 
by  all,  as  knowledge  of  medicine  or  geometry  ;  (2)  possessed  by  a 
whole  species  but  not  peculiar  to  it,  as  being  a  biped  in  man  ;  (3) 
peculiar  to  a  species,  and  possessed  by  all  at  a  certain  time,  as 
turning  grey  in  old  age  ;  (4)  Aristotle's  "proprium,"  peculiar  and 


54  The  Elements  of  Propositions. 

Accidents  that  are  both  common  and  peculiar  are  often 
useful  for  distinguishing  members  of  a  class.  Distinc- 
tive dresses  or  badges,  such  as  the  gown  of  a  student, 
the  hood  of  a  D.D.,  are  accidents,  but  mark  the  class  of 
the  individual  wearer.  So  with  the  colours  of  flowers. 

Genus,  Species,  Differentia,  Proprium,  and  Accidens 
have  been  known  since  the  time  of  Porphyry  as  the 
FIVE  PREDICABLES.  They  are  really  only  terms  used 
in  dividing  and  defining.  We  shall  return  to  them 
and  endeavour  to  show  that  they  have  no  significance 
except  with  reference  to  fixed  schemes,  scientific  or 
popular,  of  Division  or  Classification. 

Given  such  a  fixed  scheme,  very  nice  questions 
may  be  raised  as  to  whether  a  particular  attribute  is 
a  defining  attribute,  or  a  proprium,  or  an  accident,  or 
an  inseparable  accident.  Such  questions  afford  great 
scope  for  the  exercise  of  the  analytic  intellect. 

We  shall  deal  more  particularly  with  degrees  of 
generality  when  we  come  to  Definition.  This  much 
has  been  necessary  to  explain  an  unimportant  but 
much  discussed  point  in  Logic,  what  is  known  as 
the  inverse  variation  of  Connotation  and  'Denotation. 

Connotation  and  Denotation  are  often  said  to  vary 
inversely  in  quantity.  The  larger  the  connotation  the 
smaller  the  denotation,  and  vice  versd.  With  certain 
qualifications  the  statement  is  correct  enough,  but  it 
is  a  rough  compendious  way  of  expressing  the  facts 
and  it  needs  qualification. 

The  main   fact  to  be  expressed   is  that   the    more 

possessed  by  all,  as  risibility.  The  idea  of  the  Proprium  as 
deducible  from  or  consequent  on  the  essence  would  seem  to 
have  originated  in  the  desire  to  find  something  common  to  all 
Porphyry's  four  varieties. 


General  Names  and  Allied  Distinctions.  55 

general  a  name  is,  the  thinner  is  its  meaning.  The 
wider  the  scope,  the  shallower  the  ground.  As  you 
rise  in  the  scale  of  generality,  your  classes  are  wider 
but  the  number  of  common  attributes  is  less.  Inversely, 
the  name  of  a  species  has  a  smaller  denotation  than 
the  name  of  its  genus,  but  a  richer  connotation,  fruit- 
tree  applies  to  fewer  objects  than  tree,  but  the  objects 
denoted  have  more  in  common  :  so  with  apple  and 
fruit-tree,  Ribston  Pippin  and  apple. 

Again,  as  a  rule,  if  you  increase  the  connotation  you 
contract  the  area  within  which  the  name  is  applicable. 
Take  any  group  of  things  having  certain  attributes  in 
common,  say,  men  of  ability :  add  courage,  beauty,  height 
of  six  feet,  chest  measurement  of  40  inches,  and  with  each 
addition  fewer  individuals  are  to  be  found  possessing 
all  the  common  attributes. 

This  is  obvious  enough,  and  yet  the  expression  inverse 
variation  is  open  to  objection.  For  the  denotation  may 
be  increased  in  a  sense  without  affecting  the  connotation. 
The  birth  of  an  animal  may  be  said  to  increase  the 
denotation  :  every  year  thousands  of  new  houses  are 
built :  there  are  swarms  of  flies  in  a  hot  summer  and 
few  in  a  cold.  But  all  the  time  the  connotation  of 
animal,  house,  or  fly  remains  the  same  :  the  word  does 
not  change  its  meaning. 

It  is  obviously  wrong  to  say  that  they  vary  in  inverse 
proportion.  Double  or  treble  the  number  of  attributes, 
and  you  do  not  necessarily  reduce  the  denotation  by 
one-half  or  one-third. 

It  is,  in  short,  the  meaning  or  connotation  that  is 
the  main  thing.  This  determines  the  application  of  a 
word.  As  a  rule  if  you  increase  meaning,  you  restrict 
scope.  Let  your  idea,  notion,  or  concept  of  culture 
be  a  knowledge  of  Mathematics,  Latin  and  Greek  : 


56  The  Elements  of  Propositions. 

your  men  of  culture  will  be  more  numerous  than  if  you 
require  from  each  of  them  these  qualifications  plus  a 
modern  language,  an  acquaintance  with  the  Fine  Arts, 
urbanity  of  manners,  etc. 

It  is  just  possible  to  increase  the  connotation  without 
decreasing  the  denotation,  to  thicken  or  deepen  the 
concept  without  diminishing  the  class.  This  is  possible 
only  when  two  properties  are  exactly  co-extensive,  as 
equilaterality  and  equiangularity  in  triangles. 

Singular  and  Proper  Names.  A  Proper  or  Singular 
name  is  a  name  used  to  designate  an  individual.  Its 
function,  as  distinguished  from  that  of  the  general 
name,  is  to  be  used  purely  for  the  purpose  of  distinctive 
reference. 

A  man  is  not  called  Tom  or  Dick  because  he  is  like 
in  certain  respects  to  other  Toms  or  other  Dicks.  The 
Toms  or  the  Dicks  do  not  form  a  logical  class.  The 
names  are  given  purely  for  purposes  of  distinction,  to 
single  out  an  individual  subject.  The  Arabic  equivalent 
for  a  Proper  name,  atam,  "  a  mark,"  "  a  sign-post,"  is 
a  recognition  of  this. 

In  the  expressions  "a  Napoleon,"  "a  Hotspur,"  "a 
Harry,"  the  names  are  not  singular  names  logically, 
but  general  names  logically,  used  to  signify  the  posses- 
sion of  certain  attributes. 

A  man  may  be  nicknamed  on  a  ground,  but  if  the 
name  sticks  and  is  often  used,  the  original  meaning  is 
forgotten.  If  it  suggests  the  individual  in  any  one  of 
his  qualities,  any  point  in  which  he  resembles  other 
individuals,  it  is  no  longer  a  Proper  or  Singular  name 
logically,  that  is,  in  logical  function.  That  function 
is  fulfilled  when  it  has  called  to  mind  the  individual 
intended. 

To  ask,  as  is  sometimes  done,  whether  Proper  names 


General  Names  and  Allied  Distinctions.          57 

are  connotative  or  denotative,  is  merely  a  confusion  of 
language.  The  distinction  between  connotation  and 
denotation,  extension  and  intension,  applies  only 
to  general  names.  Unless  a  name  is  general,  it 
has  neither  extension  nor  intension : *  a  Proper  or 
Singular  name  is  essentially  the  opposite  of  a  general 
name  and  has  neither  the  one  nor  the  other. 

A  nice  distinction  may  be  drawn  between  Proper 
and  Singular  names,  though  they  are  strict  synonyms 
for  the  same  logical  function.  It  is  not  essential  to 
the  discharge  of  that  function  that  the  name  should  be 
strictly  appropriated  to  one  object.  There  are  many 
Toms  and  many  Dicks.  It  is  enough  that  the  word 
indicates  the  individual  without  confusion  in  the 
particular  circumstances. 

This  function  may  be  discharged  by  words  and 
combinations  of  words  that  are  not  Proper  in  the 
grammatical  sense.  "  This  man,"  "the  cover  of  this 
book,"  "  the  Prime  Minister  of  England,"  "  the  seer  of 

1  It  is  a  plausible  contention  that  in  the  case  of  the  Singular 
name  the  extension  is  at  a  minimum  and  the  intension  at  a 
maximum,  the  extension  being  one  individual,  and  the  intension 
the  totality  of  his  attributes.  But  this  is  an  inexact  and  confused 
use  of  words.  A  name  does  not  extend  beyond  the  individual 
except  when  it  is  used  to  signify  one  or  more  of  his  prominent 
qualities,  that  is,  is  used  with  the  function  of  a  general  name. 
The  £*tension  of  a  Singular  name  is  zero  :  it  has  no  extension. 
On  the  other  hand,  it  suggests,  in  its  function  as  a  Singular  name, 
no  properties  or  qualities  ;  it  suggests  only  a  subject ;  i.e.,  it  has 
no  intension.  The  ambiguity  of  the  term  Denotation  helps  the 
confusion  in  the  case  of  Singular  names.  "  Denote  "  in  common 
speech  means  to  indicate,  to  distinguish.  But  when  in  Logic  we 
say  that  a  general  name  denotes  individuals,  we  have  no  thought 
of  indicating  or  distinguishing :  we  mean  only  that  it  is  applicable 
to  any  one,  without  respect  of  individuals,  either  in  predication  or 
epithetic  description. 


58  The  Elements  of  Propositions. 

Chelsea,"  may  be  Singular  names  as  much  as  Honolulu 
or  Lord  Tennyson. 

In  common  speech  Singular  names  are  often 
manufactured  ad  hoc  by  taking  a  general  name  and 
narrowing  it  down  by  successive  qualifications  till  it 
applies  only  to  one  individual,  as  "The  leading  subject 
of  the  Sovereign  of  England  at  the  present  time".  If 
it  so  happens  that  an  individual  has  some  attribute  or 
combination  peculiar  to  himself,  he  may  be  suggested 
by  the  mention  of  that  attribute  or  combination  : — 
"the  inventor  of  the  steam-engine,"  "the  author  of 
Hudibras  ". 

Have  such  names  a  connotation  ?  The  student  may 
exercise  his  wits  on  the  question.  It  is  a  nice  one,  an 
excellent  subject  of  debate.  Briefly,  if  we  keep  rigid 
hold  of  the  meaning  of  connotation,  this  Singular  name 
has  none.  The  combination  is  a  singular  name  only 
when  it  is  the  subject  of  a  predication  or  an  attribution, 
as  in  the  sentences,  "The  position  of  the  leading  subject 
of  etc.,  is  a  difficult  one,"  or  "The  leading  subject  of 
etc.,  wears  an  eyeglass".  In  such  a  sentence  as 
"  So-and-so  is  the  leading  subject  of  etc.,"  the 
combined  name  has  a  connotation,  but  then  it  is  a 
general  and  not  a  singular  name. 

Collective  Names,  as  distinguished  from  General 
Names.  A  collective  name  is  a  name  for  a  number  of 
similar  units  taken  as  a  whole — a  name  for  a  totality 
of  similar  units,  as  army,  regiment,  mob,  mankind, 
patrimony,  personal  estate. 

A  group  or  collection  designated  by  a  collective  name 
is  so  far  like  a  class  that  the  individual  objects  have 
something  in  common :  they  are  not  heterogeneous 
but  homogeneous.  A  mob  is  a  collection  of  human 
beings  :  a  regiment  of  soldiers  ;  a  library  of  books. 


General  Names  and  Allied  Distinctions.          59 

The  distinction  lies  in  this,  that  whatever  is  said 
of  a  collective  name  is  said  about  the  collection  as  a 
whole,  and  does  not  apply  to  each  individual ;  what- 
ever is  said  of  a  general  name  applies  to  each 
individual.  Further,  the  collective  name  can  be 
predicated  only  of  the  whole  group,  as  a  whole ;  the 
general  name  is  predicable  of  each,  distributively. 
"  Mankind  has  been  in  existence  for  thousands  ot 
years;"  "The  mob  passed  through  the  streets." 
In  such  expressions  as  "  An  honest  man's  the  noblest 
work  of  God,"  the  subject  is  functionally  a  collective 
name. 

A  collective  name  may  be  used  as  a  general  name 
when  it  is  extended  on  the  ground  of  what  is  common 
to  all  such  totalities  as  it  designates.  "  An  excited 
mob  is  dangerous ;  "  "  An  army  without  discipline  is 
useless."  The  collective  name  is  then  "  connotative  " 
of  the  common  characters  of  the  collection. 

Material  or  Substantial  Names.  The  question 
has  been  raised  whether  names  of  material,  gold, 
water,  snow,  coal,  are  general  or  collective  singular. 
In  the  case  of  pieces  or  bits  of  a  material,  it  is  true  that 
any  predicate  made  concerning  the  material,  such  as 
"  Sugar  is  sweet,"  or  "  Water  quenches  thirst,"  applies 
to  any  and  every  portion.  But  the  separate  portions 
are  not  individuals  in  the  whole  signified  by  a  material 
name  as  individuals  are  in  a  class.  Further,  the  name 
of  material  cannot  be  predicated  of  a  portion  as  a  class 
name  can  be  of  an  individual.  We  cannot  say,  "  This 
is  a  sugar  ".  When  we  say,  "  This  is  a  piece  of  sugar," 
sugar  is  a  collective  name  for  the  whole  material. 
There  are  probably  words  on  the  borderland  between 
general  names  and  collective  names.  In  such  expres- 
sions as  "  This  is  a  coal"  "  The  bonnie  water  o'  Urie," 


60  The  Elements  of  Propositions. 

the  material  name  is  used  as  a  general  name.  The 
real  distinction  is  between  the  distributive  use  and  the 
collective  use  of  a  name ;  as  a  matter  of  grammatical 
usage,  the  same  word  may  be  used  either  way,  but 
logically  in  any  actual  proposition  it  must  be  either 
one  or  the  other. 

Abstract  Names  are  names  for  the  common  attri- 
butes or  concepts  on  which  classes  are  constituted.  A 
concrete  name  is  a  name  directly  applicable  to  an 
individual  in  all  his  attributes,  that  is,  as  he  exists  in 
the  concrete.  It  may  be  written  on  a  ticket  and  pinned 
to  him.  When  we  have  occasion  to  speak  of  the  point 
or  points  in  which  a  number  of  individuals  resemble 
one  another,  we  use  what  is  called  an  abstract  name. 
"Generous  man,"  "  clever  man,"  "  timid  man,"  are 
concrete  names;  "generosity,"  "cleverness, ""timidity," 
are  abstract  names. 

It  is  disputed  whether  abstract  names  are  connotative. 
The  question  is  a  confused  one :  it  is  like  asking 
whether  the  name  of  a  town  is  municipal.  An  abstract 
name  is  the  name  of  a  connotation  as  a  separate 
object  of  thought  or  reference,  conceived  or  spoken  of 
in  abstraction  from  individual  accidents.  Strictly 
speaking  it  is  notative  rather  than  iwmotative  :  it  can- 
not be  said  to  have  a  connotation  because  it  is  itself 
the  symbol  of  what  is  called  the  connotation  of  a 
general  name.1 

1  Strictly  speaking,  as  I  have  tried  to  indicate  all  along,  the 
words  Connotation  and  Denotation,  or  Extension  and  Intension, 
apply  only  to  general  names.  Outside  general  names,  they  have 
no  significance.  An  adjective  with  its  noun  is  a  general  name,  of 
which  the  adjective  gives  part  of  the  Connotation.  If  we  apply 
the  word  connotation  to  signify  merely  the  suggestion  of  an 
attribute  in  whatever  grammatical  connexion,  then  an  abstract 


General  Names  and  Allied  Distinctions.          61 

The  distinction  between  abstract  names  and  concrete 
names  is  virtually  a  grammatical  distinction,  that  is, 
a  distinction  in  mode  of  predication.  We  may  use 
concrete  names  or  abstract  names  at  our  pleasure  to 
express  the  same  meaning.  To  say  that  "  John 
is  a  timid  man "  is  the  same  thing  as  saying  that 
"Timidity  is  one  of  the  properties  or  characteristics 
or  attributes  of  John  ".  "  Pride  and  cruelty  generally 
go  together;  "  "  Proud  men  are  generally  cruel  men." 

General  names  are  predicable  of  individuals  because 
they  possess  certain  attributes :  to  predicate  the 
possession  of  those  attributes  is  the  same  thing  as  to 
predicate  the  general  name. 

Abstract  forms  of  predication  are  employed  in 
common  speech  quite  as  frequently  as  concrete,  and 
are,  as  we  shall  see,  a  great  source  of  ambiguity  and 
confusion. 


name  is  undoubtedly  as  much  connotative  as  an  adjective.  The 
word  Sweetness  has  the  same  meaning  as  Sweet :  it  indicates  or 
signifies,  conveys  to  the  mind  of  the  reader  the  same  attribute  : 
the  only  difference  is  that  it  does  not  at  the  same  time  indicate  a 
subject  in  which  the  attribute  is  found,  as  sweet  apple.  The 
meaning  is  not  connoted. 


CHAPTER  II. 

THE  SYLLOGISTIC  ANALYSIS  OF  PROPOSITIONS 
INTO  TERMS. 

I.— THE  BARE  ANALYTIC  FORMS. 

THE  word  "  term  "  is  loosely  used  as  a  mere  synonym 
for  a  name  :  strictly  speaking,  a  term  (o/oos,  a  boundary) 
is  one  of  the  parts  of  a  proposition  as  analysed  into 
Subject  and  Predicate.  In  Logic,  a  term  is  a  technical 
word  in  an  analysis  made  for  a  special  purpose,  that 
purpose  being  to  test  the  mutual  consistency  of 
propositions. 

For  this  purpose,  the  propositions  of  common 
speech  may  be  viewed  as  consisting  of  two  Terms,  a 
linkword  called  the  copula  (positive  or  negative) 
expressing  a  relation  between  them,  and  certain 
symbols  of  quantity  used  to  express  that  relation 
more  precisely. 

Let  us  indicate  the  Subject  term  by  S,  and  the 
Predicate  term  by  P. 

All  propositions  may  be  analysed  into  one  or  other 
of  four  forms  : — 

All  S  is  P, 
No  S  is  P, 
Some  S  is  P, 
Some  S  is  not  P. 
(62) 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    63 

All  S  is  P  is  called  the  Universal  Affirmative, 
and  is  indicated  by  the  symbol  A  (the  first  vowel  of 
Affirmo). 

No  S  is  P  is  called  the  Universal  Negative,  symbol 
E  (the  first  vowel  of  Nego). 

Some  S  is  P  is  called  the  Particular  Affirmative, 
symbol  I  (the  second  vowel  of  afflrmo). 

Some  S  is  not  P  is  called  the  Particular  Negative, 
symbol  O  (the  second  vowel  of  negQ). 

The  distinction  between  Universal  and  Particular 
is  called  a  distinction  in  Quantity ;  between  Affirma- 
tive and  Negative,  a  distinction  in  Quality.  A  and  E, 
I  and  O,  are  of  the  same  quantity,  but  of  different 
quality  :  A  and  I,  E  and  O,  same  in  quality,  different 
in  quantity. 

In  this  symbolism,  no  provision  is  made  for  expres- 
sing degrees  of  particular  quantity.  Some  stands  for 
any  number  short  of  all :  it  may  be  one,  few,  most, 
or  all  but  one.  The  debates  in  which  Aristotle's 
pupils  were  interested  turned  mainly  on  the  proof  or 
disproof  of  general  propositions  ;  if  only  a  proposition 
could  be  shown  to  be  not  universal,  it  did  not  matter 
how  far  or  how  little  short  it  came.  In  the  Logic  of 
Probability,  the  degree  becomes  of  importance. 

Distinguish,  in  this  Analysis,  to  avoid  subsequent 
confusion,  between  the  Subject  and  the  Subject  Term, 
the  Predicate  and  the  Predicate  Term.  The  Subject 
is  the  Subject  Term  quantified:  in  A  and  E,1  "All  S"; 

1  For  perfect  symmetry,  the  form  of  E  should  be  All  S  is  not  P. 
"  No  S  is  P  "  is  adopted  for  E  to  avoid  conflict  with  a  form  of 
common  speech,  in  which  All  S  is  not  P  conveys  the  meaning  of 
the  Particular  Negative.  "  All  advices  are  not  safe  "  does  not 
mean  that  safeness  is  denied  of  all  advices,  but  that  safeness 
cannot  be  affirmed  of  all,  i.e..  Not  all  advices  are  safe,  i.e.,  some 
are  not. 


64 


The  Elements  of  Propositions. 


in  I  and  O,  "  Some  S".  The  Predicate  is  the  Predi- 
cate Term  with  the  Copula,  positive  or  negative :  in 
A  and  I,  "  is  P  "  ;  in  E  and  O,  "  is  not  P  ". 

It  is  important  also,  in  the  interest  of  exactness,  to 
note  that  S  and  P,  with  one  exception,  represent 
general  names.  They  are  symbols  for  classes.  P  is 
so  always  :  S  also  except  when  the  Subject  is  an 
individual  object.  In  the  machinery  of  the  Syllogism, 
predications  about  a  Singular  term  are  treated  as 
Universal  Affirmatives.  "  Socrates  is  a  wise  man  >r 
is  of  the  form  All  S  is  P. 

S  and  P  being  general  names,  the  signification  of 
the  symbol  "  is "  is  not  the  same  as  the  "  is "  of 
common  speech,  whether  the  substantive  verb  or  the 
verb  of  incomplete  predication.  In  the  syllogistic 
form,  "  is "  means  is  contained  in,  "  is  not,"  is  not 
contained  in. 

The  relations  between  the  terms  in  the  four  forms 
are  represented  by  simple  diagrams  known  as  Euler's 
circles. 


Diagram  5  is  a  purely  artificial  form,  having  no 
representative  in  common  speech.  In  the  affirmations 
of  common  speech,  P  is  always  a  term  of  greater 
extent  than  S. 

No.  2  represents   the  special  case  where  S  and   P 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    65 

are  coextensive,  as  in  All  equiangular  triangles  are 
equilateral. 

S  and  P  being  general  names,  they  are  said  to  be 
distributed  when  the  proposition  applies  to  them  in 
their  whole  extent,  that  is,  when  the  assertion  covers 
every  individual  in  the  class. 

In  E,  the  Universal  Negative,  both  terms  are 
distributed:  "  No  S  is  P "  wholly  excludes  the  two 
classes  one  from  the  other,  imports  that  not  one 
individual  of  either  is  in  the  other. 

In  A,  S  is  distributed,  but  not  P.  S  is  wholly  in 
P.  but  nothing  is  said  about  the  extent  of  P  beyond  S. 

In  O,  S  is  undistributed,  P  is  distributed.  A  part  of 
S  is  declared  to  be  wholly  excluded  from  P. 

In  I,  neither  S  nor  P  is  distributed. 

It  will  be  seen  that  the  Predicate  term  of  a  Negative 
proposition  is  always  distributed,  of  an  Affirmative, 
always  undistributed. 

A  little  indistinctness  in  the  signification  of  P  crept 
into  mediaeval  text-books,  and  has  tended  to  confuse 
modern  disputation  about  the  import  of  Predication. 
Unless  P  is  a  class  name,  the  ordinary  doctrine  of 
distribution  is  nonsense  ;  and  Euler's  diagrams  are 
meaningless.  Yet  many  writers  who  adopt  both 
follow  mediaeval  usage  in  treating  P  as  the  equivalent 
of  an  adjective,  and  consequently  "  is  "  as  identical 
with  the  verb  of  incomplete  predication  in  common 
speech. 


It  should  be  recognised  that  these  syllogistic  forms 
are  purely  artificial,  invented  for  a  purpose,  namely, 
the  simplification  of  syllogising.  Aristotle  indicated 
the  precise  usage  on  which  his  syllogism  is  based 

5 


66  The  Elements  of  Propositions. 

(Prior  Analytics,  i.  I  and  4).  His  form  1  for  All  S  is 
P,  is  S  is  wholly  in  P  ;  for  No  S  is  P,  S  is  wholly  not 
in  P.  His  copula  is  not  "  is,"  but  "  is  in,"  and  it  is 
a  pity  that  this  usage  was  not  kept.  "All  S  is  in  P  " 
would  have  saved  much  confusion.  But>  doubtless 
for  the  sake  of  simplicity,  the  besetting  sin  of  tutorial 
handbooks,  All  S  is  P  crept  in  instead,  illustrated  by 
such  examples  as  "All  men  are  mortal". 

Thus  the  "  is  "  of  the  syllogistic  form  became  confused 
with  the  "  is  "  of  common  speech,  and  the  syllogistic 
view  of  predication  as  being  equivalent  to  inclusion  in, 
or  exclusion  from  a  class,  was  misunderstood.  The 
true  Aristotelian  doctrine  is  not  that  predication 
consists  in  referring  subjects  to  classes,  but  only  that 
for  certain  logical  purposes  it  may  be  so  regarded. 
The  syllogistic  forms  are  artificial  forms.  They 
were  not  originally  intended  to  represent  the  actual 
processes  of  thought  expressed  in  common  speech. 
To  argue  that  when  I  say  "All  crows  are  black,"  I 
do  not  form  a  class  of  black  things,  and  contemplate 
crows  within  it  as  one  circle  is  within  another,  is  to 
contradict  no  intelligent  logical  doctrine. 

The  root  of  the  confusion  lies  in  quoting  sentences 
from  common  speech  as  examples  of  the  logical  forms, 
forgetting  that  those  forms  are  purely  artificial. 
"  Omnis  homo  est  mortalis,"  "  All  men  are  mortal," 
is  not  an  example  formally  of  All  S  is  P.  P  is  a 
symbol  for  a  substantive  word  or  combination  of 
words,  and  mortal  is  an  adjective.  Strictly  speaking, 
there  is  no  formal  equivalent  in  common  speech,  that 
is,  in  the  forms  of  ordinary  use — no  strict  grammatical 

1  His  most  precise  form,  I  should  say,  for  in  "  P  is  predicated 
of  every  S  "  he  virtually  follows  common  speech. 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    67 

formal  equivalent — for  the  syllogistic  prepositional 
symbols.  We  can  make  an  equivalent,  but  it  is  not 
a  form  that  men  would  use  in  ordinary  intercourse. 
"  All  man  is  in  mortal  being "  would  be  a  strict 
equivalent,  but  it  is  not  English  grammar. 

Instead  of  disputing  confusedly  whether  All  S  is  P 
should  be  interpreted  in  extension  or  in  comprehension, 
it  would  be  better  to  recognise  the  original  and  tradi- 
tional use  of  the  symbols  S  and  P  as  class  names,  and 
employ  other  symbols  for  the  expression  in  compre- 
hension or  connotation.  Thus,  let  s  and  p  stand  for 
the  connotation.  Then  the  equivalent  for  All  S  is 
P  would  be  All  S  has/,  or/  always  accompanies  s,  or 
p  belongs  to  all  S. 

It  may  be  said  that  if  predication  is  treated  in  this 
way,  Logic  is  simplified  to  the  extent  of  childishness. 
And  indeed,  the  manipulation  of  the  bare  forms  with 
the  help  of  diagrams  and  mnemonics  is  a  very  humble 
exercise.  The  real  discipline  of  Syllogistic  Logic  lies 
in  the  reduction  of  common  speech  to  these  forms. 

This  exercise  is  valuable  because  it  promotes  clear 
ideas  about  the  use  of  general  names  in  predication, 
their  ground  in  thought  and  reality,  and  the  liabilities 
to  error  that  lurk  in  this  fundamental  instrument  of 
speech. 

II. — THE  PRACTICE  OF  SYLLOGISTIC  ANALYSIS. 
The  basis  of  the  analysis  is  the  use  of  general  names 
in  predication.  To  say  that  in  predication  a  subject  is 
referred  to  a  class,  is  only  another  way  of  saying  that 
in  every  categorical  sentence  the  predicate  is  a  general 
name  express  or  implied  :  that  it  is  by  means  of 
general  names  that  we  convey  our  thoughts  about 
things  to  others. 


68  The  Elements  of  Propositions, 

"  Milton  is  a  great  poet."  "  Quoth  Hudibras, 
/  smell  a  rat''  Great  poet  is  a  general  name  :  it  means 
certain  qualities,  and  applies  to  anybody  possessing 
them.  Quoth  implies  a  general  name,  a  name  for 
persons  speaking,  connoting  or  meaning  a  certain  act 
and  applicable  to  anybody  in  the  performance  of  it. 
Quoth  expresses  also  past  time  :  thus  it  implies  another 
general  name,  a  name  for  persons  in  past  time,  conno- 
ting a  quality  which  differentiates  a  species  in  the  genus 
persons  speaking,  and  making  the  predicate  term 
"  persons  speaking  in  past  time  ".  Thus  the  proposi- 
tion Quoth  Hudibras,  analysed  into  the  syllogistic 
form  S  is  in  P,  becomes  S  (Hudibras)  is  in  P  (persons 
speaking  in  past  time).  The  Predicate  term  P  is  a 
class  constituted  on  those  properties.  Smell  a  rat  also 
implies  a  general  name,  meaning  an  act  or  state 
predicable  of  many  individuals. 

Even  if  we  add  the  grammatical  object  of  Quoth  to 
the  analysis,  the  Predicate  term  is  still  a  general  name. 
Hudibras  is  only  one  of  the  persons  speaking  in  past 
time  who  have  spoken  of  themselves  as  being  in  a 
certain  mood  of  suspicion.1 

The  learner  may  well  ask  what  is  the  use  of  twisting 

1  Remember  that  when  we  speak  of  a  general  name,  we  do  not 
necessarily  mean  a  single  word.  A  general  name,  logically 
viewed,  is  simply  the  name  of  a  genus,  kind,  or  class :  and 
whether  this  is  single-worded  or  many-worded  is,  strictly 
speaking,  a  grammatical  question.  "Man,"  "  man-of-ability, " 
"  man-of-ability-and-courage,"  "  man-of-ability-and-courage-and- 
gigantic-stature, "  "  man-who-fought-at-Marathon  "—these  are 
all  general  names  in  their  logical  function.  No  matter  how  the 
constitutive  properties  of  the  class  are  indicated,  by  one  word  or 
by  a  combination,  that  word  or  combination  is  a  general  name. 
In  actual  speech  we  can  seldom  indicate  by  a  single  word  the 
meaning  predicated. 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    69 

plain  speech  into  these  uncouth  forms.  The  use  is 
certainly  not  obvious.  The  analysis  may  be  directly 
useful,  as  Aristotle  claimed  for  it,  when  we  wish 
to  ascertain  exactly  whether  one  proposition  contra- 
dicts another,  or  forms  with  another  or  others  a  valid 
link  in  an  argument.  This  is  to  admit  that  it  is 
only  in  perplexing  cases  that  the  analysis  is  of  direct 
use.  The  indirect  use  is  to  familiarise  us  with 
what  the  forms  of  common  speech  imply,  and  thus 
strengthen  the  intellect  for  interpreting  the  condensed 
and  elliptical  expression  in  which  common  speech 
abounds. 

There  are  certain  technical   names  applied  to  the 
components   of  many-worded   general    names,    Gate 
gorematic    and    Syncategorematic,    Subject    and 
Attributive.     The  distinctions  are  really  grammatical 
rather  than  logical,  and  of  little  practical  value. 

A  word  that  can  stand  by  itself  as  a  term  is  said  to 
be  Categorematic.  Man,  poet,  or  any  other  common 
noun. 

A  word  that  can  only  form  part  of  a  term  is 
Syncategorematic.  Under  this  definition  come  all 
adjectives  and  adverbs. 

The  student's  ingenuity  may  be  exercised  in  applying 
the  distinction  to  the  various  parts  of  speech.  A  verb 
may  be  said  to  be  Hypercategorematic,  implying,  as  it 
does,  not  only  a  term,  but  also  a  copula. 

A  nice  point  is  whether  the  Adjective  is  cate- 
gorematic  or  Syncategorematic.  The  question  depends 
on  the  definition  of  "  term  "  in  Logic.  In  common 
speech  an  adjective  may  stand  by  itself  as  a  predicate, 
and  so  might  be  said  to  be  Categorematic.  "  This 
heart  is  merry."  But  if  a  term  is  a  class,  or  the  name 
of  a  class,  it  is  not  Categorematic  in  the  above 


yo  The  Elements  of  Propositions. 

definition.  It  can  only  help  to  specify  a  class  when 
attached  to  the  name  of  a  higher  genus. 

Mr.  Fowler's  words  Subject  and  Attributive 
express  practically  the  same  distinction,  except  that 
Attributive  is  of  narrower  extent  than  syncategorematic. 
An  Attributive  is  a  word  that  connotes  an  attribute  or 
property,  as  hot,  valorous,  and  is  always  grammatically 
an  adjective. 

The  expression  of  Quantity,  that  is,  of  Universality 
or  non-universality,  is  all-important  in  syllogistic 
formulas.  In  them  universality  is  expressed  by  All 
or  None.  In  ordinary  speech  universality  is  expressed 
in  various  forms,  concrete  and  abstract,  plain  and 
figurative,  without  the  use  of  "  all  "  or  "  none  ". 

Uneasy  lies  the  head  that  wears  a  crown. 
He  can't  be  wrong  whose  life  is  in  the  right. 
What  cat's  averse  to  fish  ? 
Can  the  leopard  change  his  spots  ? 
The  longest  road  has  an  end. 
Suspicion  ever  haunts  the  guilty  mind. 
Irresolution  is  always  a  sign  of  weakness. 
Treason  never  prospers. 

A  proposition  in  which  the  quantity  is  not  expressed 
is  called  by  Aristotle  Indefinite  (dStopto-ros).  For 
"  indefinite " *  Hamilton  suggests  Preindesignate, 

1  The  objection  taken  to  the  word  "indefinite,"  that  the 
quantity  of  particular  propositions  is  indefinite,  some  meaning 
any  quantity  less  than  all,  is  an  example  of  the  misplaced  and 
frivolous  subtlety  that  has  done  so  much  to  disorder  the  tradition 
of  Logic.  By  "  indefinite "  is  simply  meant  not  definitely 
expressed  as  either  Universal  or  Particular,  Total  or  Partial. 
The  same  objection  might  be  taken  to  any  word  used  to  express 
the  distinction :  the  degree  of  quantity  in  Some  S  is  not 
"  designate  "  any  more  than  it  is  "  definite  "  or  "  dioristic  ". 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    71 

undesignated,  that  is,  before  being  received  from  common 
speech  for  the  syllogistic  mill.  A  proposition  is 
Predesignate  when  the  quantity  is  definitely  indicated. 
All  the  above  propositions  are  "  Predesignate  "  uni- 
versals,  and  reducible  to  the  form  All  S  is  P,  or  No 
S  is  P. 

The  following  propositions  are  no  less  definitely 
particular,  reducible  to  the  form  I  or  O.  In  them  as 
in  the  preceding  quantity  is  formally  expressed,  though 
the  forms  used  are  not  the  artificial  syllogistic  forms  : — 

Afflictions  are  often  salutary. 
Not  every  advice  is  a  safe  one. 
All  that  glitters  is  not  gold. 
Rivers  generally1  run  into  the  sea. 

Often,  however,  it  is  really  uncertain  from  the  form 
of  common  speech  whether  it  is  intended  to  express  a 
universal  or  a  particular.  The  quantity  is  not  formally 
expressed.  This  is  especially  the  case  with  proverbs 
and  loose  floating  sayings  of  a  general  tendency.  For 
example : — 

Haste  makes  waste. 

Knowledge  is  power. 

Light  come,  light  go. 

Left-handed  men  are  awkward  antagonists. 

Veteran  soldiers  are  the  steadiest  in  fight. 

^•Generally.  In  this  word  we  have  an  instance  of  the  frequent  con- 
flict between  the  words  of  common  speech  and  logical  terminology. 
How  it  arises  shall  be  explained  in  next  chapter.  A  General  pro- 
position is  a  synonym  for  a  Universal  proposition  (if  the  forms  A 
and  E  are  so  termed) :  but  "  generally  "  in  common  speech  means 
"for  the  most  part,"  and  is  represented  by  the  symbol  of  par- 
ticular quantity,  Some. 


72  The  Elements  of  Propositions. 

Such  sayings  are  in  actual  speech  for  the  most  part 
delivered  as  universals.1  It  is  a  useful  exercise  of  the 
Socratic  kind  to  decide  whether  they  are  really  so. 
This  can  only  be  determined  by  a  survey  of  facts.  The 
best  method  of  conducting  such  a  survey  is  probably 
(i)  to  pick  out  the  concrete  subject,  "  hasty  actions," 
"men  possessed  of  knowledge,"  "things  lightly 
acquired  " ;  (2)  to  fix  the  attribute  or  attributes  predi- 
cated ;  (3)  to  run  over  the  individuals  of  the  subject 
class  and  settle  whether  the  attribute  is  as  a  matter  of 
fact  meant  to  be  predicated  of  each  and  every  one. 

This  is  the  operation  of  Induction.  If  one  individual 
can  be  found  of  whom  the  attribute  is  not  meant  to  be 
predicated,  the  proposition  is  not  intended  as  Uni- 
versal. 

Mark  the  difference  between  settling  what  is  intended 
and  settling  what  is  true.  The  conditions  of  truth  and 
the  errors  incident  to  the  attempt  to  determine  it,  are 
the  business  of  the  Logic  of  Rational  Belief,  commonly 
entitled  Inductive  Logic.  The  kind  of  "induction" 
here  contemplated  has  for  its  aim  merely  to  determine 
the  quantity  of  a  proposition  in  common  acceptation, 
which  can  be  done  by  considering  in  what  cases  the 
proposition  would  generally  be  alleged.  This  corre- 
sponds nearly  as  we  shall  see  to  Aristotelian  Induction, 
the  acceptance  of  a  universal  statement  when  no 
instance  to  the  contrary  is  alleged. 

It  is  to  be  observed  that  for  this  operation  we  do  not 

1  With  some  logicians  it  is  a  mechanical  rule  in  reducing  to 
syllogistic  form  to  treat  as  I  or  O  all  sentences  in-  which  there  is 
no  formal  expression  of  quantity.  This  is  to  err  on  the  safe  side, 
but  common  speakers  are  not  so  guarded,  and  it  is  to  be  presumed 
rather  that  they  have  a  universal  application  in  their  minds  when 
they  do  not  expressly  qualify. 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    73 

practically  use  the  syllogistic  form  All  S  is  P.  We  do 
not  raise  the  question  Is  All  S,  P  ?  That  is,  we  do  not 
constitute  in  thought  a  class  P  :  the  class  in  our  minds 
is  S,  and  what  we  ask  is  whether  an  attribute  predicated 
of  this  class  is  truly  predicated  of  every  individual 
of  it. 

Suppose  we  indicate  by  p  the  attribute,  knot  of 
attributes,  or  concept  on  which  the  class  P  is  consti- 
tuted, then  All  S  is  P  is  equivalent  to  "  All  S  has/  "  : 
and  Has  All  S  p  ?  is  the  form  of  a  question  that  we 
have  in  our  minds  when  we  make  an  inductive  survey 
on  the  above  method.  I  point  this  out  to  emphasise 
the  fact  that  there  is  no  prerogative  in  the  form  All  S 
is  P  except  for  syllogistic  purposes. 

This  inductive  survey  may  be  made  a  useful 
Collateral  Discipline.  The  bare  forms  of  Syllogistic 
are  a  useless  item  of  knowledge  unless  they  are 
applied  to  concrete  thought.  And  determining  the 
quantity  of  a  common  aphorism  or  saw,  the  limits 
within  which  it  is  meant  to  hold  good,  is  a  valuable 
discipline  in  exactness  of  understanding.  In  trying 
to  penetrate  to  the  inner  intention  of  a  loose  general 
maxim,  we  discover  that  what  it  is  really  intended 
to  assert  is  a  general  connexion  of  attributes,  and  a 
survey  of  concrete  cases  leads  to  a  more  exact  ap- 
prehension of  those  attributes.  Thus  in  considering 
whether  Knowledge  is  power  is  meant  to  be  asserted 
of  all  knowledge,  we  encounter  along  with  such 
examples  as  the  sailor's  knowledge  that  wetting  a 
rope  shortens  it,  which  enabled  some  masons  to  raise 
a  stone  to  its  desired  position,  or  the  knowledge  of 
French  roads  possessed  by  the  German  invaders, — 
along  with  such  examples  as  these  we  encounter  cases 
where  a  knowledge  of  difficulties  without  a  knowledge 


74  The  Elements  of  Propositions. 

of  the  means  of  overcoming  them  is  paralysing  to 
action.     Samuel  Daniel  says  : — 

Where  timid  knowledge  stands  considering 
Audacious  ignorance  has  done  the  deed. 

Studying  numerous  cases  where  "  Knowledge  is 
power"  is  alleged  or  denied,  we  find  that  what  is 
meant  is  that  a  knowledge  of  the  right  means  of 
doing  anything  is  power — in  short,  that  the  predicate 
is  not  made  of  all  knowledge,  but  only  of  a  species 
of  knowledge. 

Take,  again,  Custom  blunts  sensibility.  Putting  this 
in  the  concrete,  and  inquiring  what  predicate  is  made 
about  "men  accustomed  to  anything"  (S),  we  have 
no  difficulty  in  finding  examples  where  such  men  are 
said  to  become  indifferent  to  it.  We  find  such  illus- 
trations as  Lovelace's  famous  "Paradox": — 

Through  foul  we  follow  fair 

For  had  the  world  one  face 
And  earth  been  bright  as  air 

We  had  known  neither  place. 
Indians  smell  not  their  nest 
The  Swiss  and  Finn  taste  best 

The  spices  of  the  East. 

So  men  accustomed  to  riches  are  not  acutely  sensible 
of  their  advantages :  dwellers  in  noisy  streets  cease  to 
be  distracted  by  the  din :  the  watchmaker  ceases  to 
hear  the  multitudinous  ticking  in  his  shop  :  the 
neighbours  of  chemical  works  are  not  annoyed  by  the 
smells  like  the  casual  passenger.  But  we  find  also 
that  wine-tasters  acquire  by  practice  an  unusual 
delicacy  of  sense ;  that  the  eyes  once  accustomed  to 
a  dim  light  begin  to  distinguish  objects  that  were  at 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    75 

first  indistinguishable;  and  so  on.  What  meanings 
of  "  custom  "  and  of  "  sensibility  "  will  reconcile  these 
apparently  conflicting  examples  ?  What  are  the  exact 
attributes  signified  by  the  names  ?  We  should  probably 
find  that  by  sensibility  is  meant  emotional  sensibility 
as  distinguished  from  intellectual  discrimination,  and 
that  by  custom  is  meant  familiarity  with  impressions 
whose  variations  are  not  attended  to,  or  subjection  to 
one  unvarying  impression. 

To  verify  the  meaning  of  abstract  proverbs  in  this 
way  is  to  travel  over  the  road  by  which  the  Greek 
dialecticians  were  led  to  feel  the  importance  of 
definition.  Of  this  more  will  be  said  presently.  If 
it  is  contended  that  such  excursions  are  beyond  the 
bounds  of  Formal  Logic,  the  answer  is  that  the 
exercise  is  a  useful  one  and  that  it  starts  naturally 
and  conveniently  from  the  formulas  of  Logic.  It  is  the 
practice  and  discipline  that  historically  preceded  the 
Aristotelian  Logic,  and  in  the  absence  of  which  the 
Aristotelian  formulae  would  -have  a  narrowing  and 
cramping  effect. 

Can  all  propositions  be  reduced  to  the  syllogistic 
form  ?  Probably:  but  this  is  a  purely  scientific  inquiry, 
collateral  to  Practical  Logic.  The  concern  of  Practical 
Logic  is  chiefly  with  forms  of  proposition  that  favour 
inaccuracy  or  inexactness  of  thought.  When  there  is 
no  room  for  ambiguity  or  other  error,  there  is  no  virtue 
in  artificial  syllogistic  form.  The  attempt  so  to  reduce 
any  and  every  proposition  may  lead,  however,  to  the 
study  of  what  Mr.  Bosanquet  happily  calls  the 
"  Morphology "  of  Judgment,  Judgment  being  the 
technical  name  for  the  mental  act  that  accompanies 
the  utterance  of  a  proposition.  Even  in  such  sentences 
as  "  How  hot  it  is  !  "  or  "  It  rains,"  the  rudiment  of 


7  6  The  Elements  of  Propositions. 

subject  and  predicate  may  be  detected.  When  a  man 
says  "  How  hot  it  is,"  he  conveys  the  meaning,  though 
there  is  no  definitely  formed  subject  in  his  mind,  that 
the  outer  world  at  the  moment  of  his  speaking  has  a 
certain  quality  or  attribute.  So  with  "  It  rains  ".  The 
study  of  such  examples  in  their  context,  however,  reveals 
the  fact  that  the  same  form  of  Common  speech  may 
cover  different  subjects  and  predicates  in  different 
connexions.  Thus  in  the  argument: — 

"  Whatever  is,  is  best. 
It  rains  :  " — 

the  Subject  is  Rain  and  the  Predicate  is  now,  "  is  at 
the  present  time,"  "  is  in  the  class  of  present  events". 


III. — SOME  TECHNICAL  DIFFICULTIES. 

The  formula  for  Exclusive  Propositions.  "  None 
but  the  brave  deserve  the  fair"  :  "  No  admittance 
except  on  business"  :  "  Only  Protestants  can  sit  on  the 
throne  of  England  ". 

These  propositions  exemplify  different  ways  in 
common  speech  of  naming  a  subject  exclusively,  the 
predication  being  made  of  all  outside  a  certain  term. 
"  None  that  are  not  brave,  etc.  ;  "  "  none  that  are  not 
on  business,  etc. ;  "  "  none  that  are  not  Protestants, 
etc.".  No  not-S  is  P.  It  is  only  about  all  outside  the 
given  term  that  the  universal  assertion  is  made  :  we 
say  nothing  universally  about  the  individuals  within 
the  term  :  we  do  not  say  that  all  Protestants  are 
eligible,  nor  that  all  persons  on  business  are  admitted, 
nor  that  every  one  of  the  brave  deserves  the  fair.  All 
that  we  say  is  that  the  possession  of  the  attribute 
named  is  an  indispensable  condition:  a  person  may 


The  Syllogistic  Analysis  of  Propositions  into   Terms.    77 

possess  the  attribute,  and  yet  on  other  grounds  may 
not  be  entitled  to  the  predicate. 

The  justification  for  taking  special  note  of  this  form 
in  Logic  is  that  we  are  apt  by  inadvertence  to  make  an 
inclusive  inference  from  it.  Let  it  be  said  that  None 
but  those  who  work  hard  can  reasonably  expect  to 
pass,  and  we  are  apt  to  take  this  as  meaning  that  all 
who  work  hard  may  reasonably  expect  to  pass.  But 
what  is  denied  of  every  Not-S  is  not  necessarily 
affirmed  of  every  S. 

The  expression  of  Tense  or  Time  in  the  Syllogistic 
Forms.  Seeing  that  the  Copula  in  S  is  P  or  S  is  in  P 
does  not  express  time,  but  only  a  certain  relation 
between  S  and  P,  the  question  arises  Where  are  we  to 
put  time  in  the  analytic  formula  ?  "  Wheat  is  dear ;  " 
"  All  had  fled  ;"  time  is  expressed  in  these  propositions, 
and  our  formula  should  render  the  whole  content  of 
what  is  given.  Are  we  to  include  it  in  the  Predicate 
term  or  in  the  Subject  term  ?  If  it  must  not  be  left 
out  altogether,  and  we  cannot  put  it  with  the  copula, 
we  have  a  choice  between  the  two  terms. 

It  is  a  purely  scholastic  question.  The  common 
technical  treatment  is  to  view  the  tense  as  part  of  the 
predicate.  "  All  had  fled,"  All  S  is  P,  i.e.,  the  whole 
subject  is  included  in  a  class  constituted  on  the 
attributes  of  flight  at  a  given  time.  It  may  be  that  the 
Predicate  is  solely  a  predicate  of  time.  "  The  Board 
met  yesterday  at  noon."  S  is  P,  /'.&,  the  meeting  of 
the  Board  is  one  of  the  events  characterised  by  having 
happened  at  a  certain  time,  agreeing  with  other  events 
in  that  respect. 

But  in  some  cases  the  time  is  more  properly  regarded 
as  part  of  the  subject.  E.g.,  "Wheat  is  dear".  S 
does  not  here  stand  for  wheat  collectively,  but  for  the 


78  The  Elements  of  Propositions. 

wheat  now  in  the  market,  the  wheat  of  the  present 
time  :  it  is  concerning  this  that  the  attribute  of  clearness 
is  predicated  ;  it  is  this  that  is  in  the  class  of  dear 
things. 

The  expression  of  Modality  in  the  Syllogistic  Forms. 
Propositions  in  which  the  predicate  is  qualified  by  an 
expression  of  necessity,  contingency,  possibility  or 
impossibility  [i.e.,  in  English  by  must,  may,  can,  or 
cannot] ,  were  called  in  Mediaeval  Logic  Modal  Proposi- 
tions. "  Two  and  two  must  make  four."  "  Grubs 
may  become  butterflies."  "  Z  can  paint."  "  Y  cannot 
fly." 

There  are  two  recognised  ways  of  reducing  such 
propositions  to  the  form  S  is  P.  One  is  to  distinguish 
between  the  Dictum  and  the  Mode,  the  proposition  and 
the  qualification  of  its  certainty,  and  to  treat  the  Dictum 
as  the  Subject  and  the  Mode  as  the  Predicate.  Thus  : 
"  That  two  and  two  make  four  is  necessary  "  ;  "  That 
Y  can  fly  is  impossible  ". 

The  other  way  is  to  treat  the  Mode  as  part  of  the 
predicate.  The  propriety  of  this  is  not  obvious  in  the 
case  of  Necessary  propositions,  but  it  is  unobjectionable 
in  the  case  of  the  other  three  modes.  Thus  :  "  Grubs 
are  things  that  have  the  potentiality  of  becoming 
butterflies";  "Z  has  the  faculty  of  painting";  "Y 
has  not  the  faculty  of  flying  ". 

The  chief  risk  of  error  is  in  determining  the  quantity 
of  the  subject  about  which  the  Contingent  or  Possible 
predicate  is  made.  When  it  is  said  that  "  Victories 
may  be  gained  by  accident,"  is  the  predicate  made 
concerning  All  victories  or  Some  only  ?  Here  we  are 
apt  to  confuse  the  meaning  of  the  contingent  assertion 
with  the  matter  of  fact  on  which  in  common  belief  it 
rests.  It  is  true  only  that  some  victories  have  been 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    79 

gained  by  accident,  and  it  is  on  this  ground  that  we 
assert  in  the  absence  of  certain  knowledge  concerning 
any  victory  that  it  may  have  been  so  gained.  The 
latter  is  the  effect  of  the  contingent  assertion  :  it  is 
made  about  any  victory  in  the  absence  of  certain 
knowledge,  that  is  to  say,  formally  about  all. 

The  history  of  Modals  in  Logic  is  a  good  illustration 
of  intricate  confusion  arising  from  disregard  of  a 
clear  traditional  definition.  The  treatment  of  them  by 
Aristotle  was  simple,  and  had  direct  reference  to  tricks 
of  disputation  practised  in  his  time.  He  specified  four 
"  modes,"  the  four  that  descended  to  mediaeval  logic, 
and  he  concerned  himself  chiefly  with  the  import 
of  contradicting  these  modals.  What  is  the  true 
contradictory  of  such  propositions  as,  "  It  is  possible 
to  be  "  (Svvarov  ctvat),  "  It  admits  of  being  ''  (evSe'xerat 
etvai),  "  It  must  be  "  (dvay/catoi/  etvai),  "  It  is  impossible 
to  be"  (dSwaroi/  eTvat)  ?  What  is  implied  in  saying 
"  No  "  to  such  propositions  put  interrogatively?  "  Is 
it  possible  for  Socrates  to  fly  ?  "  "  No."  Does  this 
mean  that  it  is  not  possible  for  Socrates  to  fly,  or  that 
it  is  possible  for  Socrates  not  to  fly  ? 

A  disputant  who  had  trapped  a  respondent  into 
admitting  that  it  is  possible  for  Socrates  not  to  fly, 
might  have  pushed  the  concession  farther  in  some 
such  way  as  this  :  "  Is  it  possible  for  Socrates  not 
to  walk  ?  "  "  Certainly."  "  Is  it  possible  for  him  to 
walk  ?  "  "  Yes."  "  When  you  say  that  it  is  possible 
for  a  man  to  do  anything  do  you  not  believe  that  it  is 
possible  for  him  to  do  it  ?  "  "  Yes."  "  But  you  have 
admitted  that  it  is  possible  for  Socrates  not  to  fly  ?  " 

It  was  in  view  of  such  perplexities  as  these  that 
Aristotle  set  forth  the  true  contradictories  of  his  four 
Modals.  We  may  laugh  at  such  quibbles  now  and 


8o  The  Elements  of  Propositions. 

wonder  that  a  grave  logician  should  have  thought 
them  worth  guarding  against.  But  historically  this 
is  the  origin  of  the  Modals  of  Formal  Logic,  and  to 
divert  the  names  of  them  to  signify  other  distinctions 
than  those  between  modes  of  qualifying  the  certainty 
of  a  statement  is  to  introduce  confusion. 

Thus  we  find  "  Alexander  was  a  great  general,"  given 
as  an  example  of  a  Contingent  Modal,  on  the  ground 
that  though  as  a  matter  of  fact  Alexander  was  so  he 
might  have  been  otherwise.  It  was  not  necessary  that 
Alexander  should  be  a  great  general :  therefore  the 
proposition  is  contingent.  Now  the  distinction  between 
Necessary  truth  and  Contingent  truth  may  be  important 
philosophically :  but  it  is  merely  confusing  to  call  the 
character  of  propositions  as  one  or  the  other  by  the 
name  of  Modality.  The  original  Modality  is  a  mode 
of  expression  :  to  apply  the  name  to  this  character  is 
to  shift  its  meaning. 

A  more  simple  and  obviously  unwarrantable  depar- 
ture from  tradition  is  to  extend  the  name  Modality  to 
any  grammatical  qualification  of  a  single  verb  in 
common  speech.  On  this  understanding  "  Alexander 
conquered  Darius  "  is  given  by  Hamilton  as  a  Pure 
proposition,  and  "Alexander  conquered  Darius  honour- 
ably "  as  a  Modal.  This  is  a  merely  grammatical 
distinction,  a  distinction  in  the  mode  of  composing  the 
predicate  term  in  common  speech.  In  logical  tradition 
Modality  is  a  mode  of  qualifying  the  certainty  of  an 
affirmation.  "  The  conquest  of  Darius  by  Alexander 
was  honourable,"  or  "Alexander  in  conquering  Darius 
was  an  honourable  conqueror,"  is  the  syllogistic  form 
of  the  proposition  :  it  is  simply  assertory,  not  qualified 
in  any  "  mode  ". 

There  is  a  similar  misunderstanding  in  Mr.  Shedden's 


The  Syllogistic  Analysis  of  Propositions  into  Terms.    81 

treatment  of  "  generally  "  as  constituting  a  Modal  hi 
such  sentences,  as  "  Rivers  generally  flow  into  the  sea  ". 
He  argues  that  as  generally  is  not  part  either  of  the 
Subject  term  or  of  the  Predicate  term,  it  must  belong 
to  the  Copula,  and  is  therefore  a  modal  qualification  ol 
the  whole  assertion.  He  overlooked  the  fact  that  the 
word  "  generally"  is  an  expression  of  Quantity:  it 
determines  the  quantity  of  the  Subject  term. 

Finally  it  is  sometimes  held  (e.g.,  by  Mr.  Venn)  that 
the  question  of  Modality  belongs  properly  to  Scientific 
or  Inductive  Logic,  and  is  out  of  place  in  Formal 
Logic.  This  is  so  far  accurate  that  it  is  for  Inductive 
Logic  to  expound  the  conditions  of  various  degrees-  of 
certainty.  The  consideration  of  Modality  is  pertinent 
to  Formal  Logic  only  in  so  far  as  concerns  special 
perplexities  in  the  expression  of  it.  The  treatment  of 
it  by  Logicians  has  been  rendered  intricate  by  torturing 
the  old  tradition  to  suit  different  conceptions  of  the  end 
and  aim  of  Logic. 


PART   II. 
DEFINITION. 

CHAPTER  I. 

IMPERFECT  UNDERSTANDING  OF  WORDS  AND  THE 
REMEDIES  THEREFOR.  —  DIALECTIC.  —  DEFINI- 
TION. 

WE  cannot  inquire  far  into  the  meaning  of  proverbs  or 
traditional  sayings  without  discovering  that  the  com- 
mon understanding  of  general  and  abstract  names  is 
loose  and  uncertain.  Common  speech  is  a  quicksand. 
Consider  how  we  acquire  our  vocabulary,  how  we 
pick  up  the  words  that  we  use  from  our  neighbours  and 
from  books,  and  why  this  is  so  soon  becomes  apparent. 
Theoretically  we  know  the  full  meaning  of  a  name 
when  we  know  all  the  attributes  that  it  connotes,  and 
we  are  not  justified  in  extending  it  except  to  objects 
that  possess  all  the  attributes.  This  is  the  logical  ideal, 
but  between  the  ought  to  be  of  Logic  and  the  is  of 
practical  life,  there  is  a  vast  difference.  How  seldom 
do  we  conceive  words  in  their  full  meaning  !  And  who 
is  to  instruct  us  in  the  full  meaning  ?  It  is  not  as  in 
the  exact  sciences,  where  we  start  with  a  knowledge  of 
fta) 


Imperfect  Understanding  of  Words.  83 

the  full  meaning.  In  Geometry,  for  example,  we  learn 
the  definitions  of  the  words  used,  point,  line,  parallel, 
etc.,  before  we  proceed  to  use  them.  But  in  common 
speech,  we  learn  words  first  in  their  application  to 
individual  cases.  Nobody  ever  defined  good  to  us,  or 
fair,  or  kind,  or  highly  educated.  We  hear  the  words 
applied  to  individual  objects :  we  utter  them  in  the 
same  connexion  :  we  extend  them  to  other  objects  that 
strike  us  as  like  without  knowing  the  precise  points 
of  likeness  that  the  convention  of  common  speech 
includes.  The  more  exact  meaning  we  learn  by 
gradual  induction  from  individual  cases.  Ugly,  beauti- 
ful, good,  bad — we  learn  the  words  first  as  applicable  to 
things  and  persons :  gradually  there  arises  a  more  or 
le«s  definite  sense  of  what  the  objects  so  designated 
have  in  common.  The  individual's  extension  of  the 
name  proceeds  upon  what  in  the  objects  has  most 
impressed  him  when  he  caught  the  word  :  this  may 
differ  in  different  individuals ;  the  usage  of  neighbours 
corrects  individual  eccentricities.  The  child  in  arms 
shouts  Da  at  the  passing  stranger  who  reminds  him 
of  his  father :  for  him  at  first  it  is  a  general  name 
applicable  to  every  man  :  by  degrees  he  learns  that 
for  him  it  is  a  singular  name. 

The  mode  in  which  words  are  learnt  and  extended 
may  be  studied  most  simply  in  the  nursery.  A  child, 
say,  has  learnt  to  say  mambro  when  it  sees  its  nurse. 
The  nurse  works  a  hand-turned  sewing  machine,  and 
sings  to  it  as  she  works.  In  the  street  the  child  sees 
an  organ-grinder  singing  as  he  turns  his  handle :  it 
calls  mambro :  the  nurse  catches  the  meaning  and  the 
child  is  overjoyed.  The  organ-grinder  has  a  monkey: 
the  child  has  an  india-rubber  monkey  toy :  it  calls  this 
also  mambro.  The  name  is  extended  to  a  monkey  in 


84  Definition. 

a  picture-book.  It  has  a  toy  musical  box  with  a 
handle :  this  also  becomes  mambro,  the  word  being 
extended  along  another  line  of  resemblance.  A  stroller 
with  a  French  riddle  comes  within  the  denotation  of 
the  word  :  a  towel-rail  is  also  called  mambro  from  some 
fancied  resemblance  to  the  fiddle.  A  very  swarthy 
hunch-back  mambro  frightens  the  child  :  this  leads  to 
the  transference  of  the  word  to  a  terrific  coalman  with 
a  bag  of  coals  on  his  back.  In  a  short  time  the  word 
has  become  a  name  for  a  great  variety  of  objects  that 
have  nothing  whatever  common  to  all  of  them,  though 
each  is  strikingly  like  in  some  point  to  a  predecessor 
in  the  series.  When  the  application  becomes  too 
heterogeneous,  the  word  ceases  to  be  of  use  as  a 
sign  and  is  gradually  abandoned,  the  most  impressive 
meaning  being  the  last  to  go.  In  a  child's  vocabulary 
where  the  word  mambro  had  a  run  of  nearly  two  years, 
its  last  use  was  as  an  adjective  signifying  ugly  or 
horrible. 

The  history  of  such  a  word  in  a  child's  language  is 
a  type  of  what  goes  on  in  the  language  of  men.  In 
the  larger  history  we  see  similar  extensions  under 
similar  motives,  checked  and  controlled  in  the  same 
way  by  surrounding  usage. 

It  is  obvious  that  to  avoid  error  and  confusion,  the 
meaning  or  connotation  of  names,  the  concepts,  should 
somehow  be  fixed :  names  cannot  otherwise  have  an 
identical  reference  in  human  intercourse.  We  may 
call  this  ideal  fixed  concept  the  Logical  Concept :  or 
we  may  call  it  the  Scientific  Concept,  inasmuch  as 
one  of  the  main  objects  of  the  sciences  is  to  attain 
such  ideals  in  different  departments  of  study.  But  in 
actual  speech  we  have  also  the  Personal  Concept, 
which  varies  more  or  less  with  the  individual  user. 


Imperfect  Understanding  of  Words.  85 

and  the  Popular  or  Vernacular  Concept,  which, 
though  roughly  fixed,  varies  from  social  sect  to  social 
sect  and  from  generation  to  generation. 

The  variations  in  Popular  Concepts  may  be  traced 
in  linguistic  history.  Words  change  with  things  and 
with  the  aspects  of  things,  as  these  change  in  public 
interest  and  importance.  As  long  as  the  attributes 
that  govern  the  application  of  words  are  simple, 
sensible  attributes,  little  confusion  need  arise :  the 
variations  are  matters  of  curious  research  for  the 
philologist,  but  are  logically  insignificant.  Murray's 
Dictionary,  or  such  books  as  Trench's  English  Past 
and  Present,  supply  endless  examples,  as  many,  indeed 
as  there  are  words  in  the  language.  Clerk  has  almost 
as  many  connotations  as  our  typical  mambro :  clerk 
in  holy  orders,  church  clerk,  town  clerk,  clerk  of 
assize,  grocer's  clerk.  In  Early  English,  the  word 
meant  "  man  in  a  religious  order,  cleric,  clergyman  "  ; 
ability  to  read,  write,  and  keep  accounts  being  a 
prominent  attribute  of  the  class,  the  word  was 
extended  on  this  simple  ground  till  it  has  ceased 
altogether  to  cover  its  original  field  except  as  a 
formal  designation.  But  no  confusion  is  caused  by 
the  variation,  because  the  property  connoted  is 
simple.1  So  with  any  common  noun  :  street,  carriage, 
ship,  house,  merchant,  lawyer,  professor.  We  might 
be  puzzled  to  give  an  exact  definition  of  such  words, 


1  Except,  perhaps,  in  new  offices  to  which  the  name  is  extended, 
such  as  Clerk  of  School  Board.  The  name,  bearing  its  most 
simple  and  common  meaning,  may  cause  popular  misapprehension 
of  the  nature  of  the  duties.  Any  uncertainty  in  meaning  may  be 
dangerous  in  practice :  elections  have  been  affected  by  the 
ambiguity  of  this  word. 


86  Definition. 

to  say  precisely  what  they  connote  in  common  usage ; 
but  the  risk  of  error  in  the  use  of  them  is  small. 

When  we  come  to  words  of  which  the  logical  con- 
cept is  a  complex  relation,  an  obscure  or  intangible 
attribute,  the  defects  of  the  popular  conception  and  its 
tendencies  to  change  and  confusion,  are  of  the  greatest 
practical  importance.  Take  such  words  as  Monarchy, 
tyranny,  civil  freedom,  freedom  of  contract,  landlord, 
gentleman,  prig,  culture,  education,  temperance,  generosity. 
Not  merely  should  we  find  it  difficult  to  give  an 
analytic  definition  of  such  words  :  we  might  be  unable 
to  do  so,  and  yet  flatter  ourselves  that  we  had  a  clear 
understanding  of  their  meaning.  But  let  two  men 
begin  to  discuss  any  proposition  in  which  any  such 
word  is  involved,  and  it  will  often  be  found  that  they 
take  the  word  in  different  senses.  If  the  relation 
expressed  is  complex,  they  have  different  sides  or  lines 
of  it  in  their  minds ;  if  the  meaning  is  an  obscure 
quality,  they  are  guided  in  their  application  of  it  by 
different  outward  signs. 

Monarchy,  in  its  original  meaning,  is  applied  to  a 
form  of  government  in  which  the  will  of  one  man  is 
supreme,  to  make  laws  or  break  them,  to  appoint  or 
dismiss  officers  of  state  and  justice,  to  determine  peace 
or  war,  without  control  of  statute  or  custom.  But 
supreme  power  is  never  thus  uncontrolled  in  reality ; 
and  the  word  has  been  extended  to  cover  governments 
in  which  the  power  of  the  titular  head  is  controlled  in 
many  different  modes  and  degrees.  The  existence  of 
a  head,  with  the  title  of  King  or  Emperor,  is  the 
simplest  and  most  salient  fact :  and  wherever  this 
exists,  the  popular  concept  of  a  monarchy  is  realised. 
The  President  of  the  United  States  has  more  real 
power  than  the  Sovereign  of  Great  Britain  ;  but  the 


Imperfect  Understanding  of  Words.  87 

one  government  is  called  a  Republic  and  the  other 
a  Monarchy.  People  discuss  the  advantages  and 
disadvantages  of  monarchy  without  first  deciding 
whether  they  take  the  word  in  its  etymological  sense 
of  unlimited  power,  or  its  popular  sense  of  titular 
kingship,  or  its  logical  sense  of  power  definitely 
limited  in  certain  ways.  And  often  in  debate, 
monarchy  is  really  a  singular  term  for  the  government 
of  Great  Britain. 

Culture,  religious,  generous •,  are  names  for  inward 
states  or  qualities  :  with  most  individuals  some  simple 
outward  sign  directs  the  application  of  the  word — it 
may  be  manner,  or  bearing,  or  routine  observances,  or 
even  nothing  more  significant  than  the  cut  of  the 
clothes  or  of  the  hair.  Small  things  undoubtedly  are 
significant,  and  we  must  judge  by  small  things  when 
we  have  nothing  else  to  go  by :  but  instead  of  trying 
to  get  definite  conceptions  for  our  moral  epithets,  and 
suspending  judgment  till  we  know  that  the  use  of  the 
epithet  is  justified,  the  trifling  superficial  sign  becomes 
for  us  practically  the  whole  meaning  of  the  word.  We 
feel  that  we  must  have  a  judgment  of  some  sort  at 
once :  only  simple  signs  are  suited  to  our  impatience. 

It  was  with  reference  to  this  state  of  things  that 
Hegel  formulated  his  paradox  that  the  true  abstract 
thinker  is  the  plain  man  who  laughs  at  philosophy  as 
what  he  calls  abstract  and  unpractical.  He  holds 
decided  opinions  for  or  against  this  or  the  other 
abstraction,  freedom,  tyranny,  revolution,  reform,  socialism, 
but  what  these  words  mean  and  within  what  limits  the 
things  signified  are  desirable  or  undesirable,  he  is  in 
too  great  a  hurry  to  pause  and  consider. 

The  disadvantages  of  this  kind  of  "  abstract"  think- 
ing are  obvious.  The  accumulated  wisdom  of  man- 


88  Definition. 

kind  is  stored  in  language.  Until  we  have  cleared  our 
conceptions,  and  penetrated  to  the  full  meaning  of 
words,  that  wisdom  is  a  sealed  book  to  us.  Wise 
maxims  are  interpreted  by  us  hastily  in  accordance 
with  our  own  narrow  conceptions.  All  the  vocables  of  a 
language  may  be  more  or  less  familiar  to  us,  and  yet 
we  may  not  have  learnt  it  as  an  instrument  of  thought. 
Outside  the  very  limited  range  of  names  for  what  we 
see  and  use  in  the  daily  routine  of  life,  food  and  clothes 
and  the  common  occupations  of  men,  words  have  little 
meaning  for  us,  and  are  the  vehicles  merely  of  thin 
preconceptions  and  raw  prejudices. 

The  remedy  for  "abstract "  thinking  is  more  thinking, 
and  in  pursuing  this  two  aims  may  be  specified  for  the 
sake  of  clearness,  though  they  are  closely  allied,  and 
progress  towards  both  may  often  be  made  by  one  and 
the  same  operation,  (i)  We  want  to  reach  a  clear  and 
full  conception  of  the  meaning  of  names  as  used  now 
or  at  a  given  time.  Let  us  call  this  the  Verification  of 
the  Meaning.  (2)  We  want  to  fix  such  conceptions, 
and  if  necessary  readjust  their  boundaries.  This  is  the 
province  of  Definition,  which  cannot  be  effectually  per- 
formed without  Scientific  Classification  or  Division. 

I. — VERIFICATION  OF  THE  MEANING — DIALECTIC. 

This  can  only  be  done  by  assembling  the  objects 
to  which  the  words  are  applied,  and  considering  what 
they  have  in  common.  To  ascertain  the  actual 
connotation  we  must  run  over  the  actual  denotation. 
And  since  in  such  an  operation  two  or  more  minds  are 
better  than  one,  discussion  or  dialectic  is  both  more 
fruitful  and  more  stimulating  than  solitary  reflection 
or  reading. 


Verification  of  Meaning.  89 

The  first  to  practise  this  process  on  a  memorable 
scale,  and  with  a  distinct  method  and  purpose,  was 
Socrates.  To  insist  upon  the  necessity  of  clear 
conceptions,  and  to  assist  by  his  dialectic  procedure 
in  forming  them,  was  his  contribution  to  philosophy. 

His  plan  was  to  take  a  common  name,  profess 
ignorance  of  its  meaning,  and  ask  his  interlocutor 
whether  he  would  apply  it  in  such  and  such  an 
instance,  producing  one  after  another.  According  to 
Xenophon's  Memorabilia  he  habitually  chose  the 
commonest  names,  good,  unjust,  fitting,  and  so  forth, 
and  tried  to  set  men  thinking  about  them,  and 
helped  them  by  his  questions  to  form  an  intelligent 
conception  of  the  meaning. 

For  example,  what  is  the  meaning  of  injustice  ? 
Would  you  say  that  the  man  who  cheats  or  deceives 
is  unjust  ?  Suppose  a  man  deceives  his  enemies,  is 
there  any  injustice  in  that  ?  Can  the  definition  be 
that  a  man  who  deceives  his  friends  is  unjust  ?  But 
there  are  cases  where  friends  are  deceived  for  their 
own  good :  are  these  cases  of  injustice  ?  A  general 
may  inspirit  his  soldiers  by  a  falsehood.  A  man 
may  cajole  a  weapon  out  of  his  friend's  hand  when 
he  sees  him  about  to  commit  suicide.  A  father  may 
deceive  his  son  into  taking  medicine.  Would  you 
call  these  men  unjust  ?  By  some  such  process  of 
interrogation  we  are  brought  to  the  definition  that 
a  man  is  unjust  who  deceives  his  friends  to  their 
hurt. 

Observe  that  in  much  of  his  dialectic  the  aim  of 
Socrates  was  merely  to  bring  out  the  meaning  lying 
vague  and  latent,  as  it  were,  in  the  common  mind. 
His  object  was  simply  what  we  have  called  the 
verification  of  the  meaning.  And  a  dialectic  that 


90  Definition. 

confines  itself  to  the  consideration  of  what  is  ordin- 
arily meant  as  distinct  from  what  ought  to  be  meantr 
may  often  serve  a  useful  purpose.  Disputes  about 
words  are  not  always  as  idle  as  is  sometimes 
supposed.  Mr.  H.  Sidgwick  truly  remarks  (a  prop  as 
of  the  terms  of  Political  Economy)  that  there  is 
often  more  profit  in  seeking  a  definition  than  in 
finding  it.  Conceptions  are  not  merely  cleared  but 
deepened  by  the  process.  Mr.  Sidgwick's  remarks 
are  so  happy  that  I  must  take  leave  to  quote  them : 
they  apply  not  merely  to  the  verification  of  ordinary 
meaning  but  also  to  the  study  of  special  uses  by 
authorities,  and  the  reasons  for  those  special  uses. 

"  The  truth  is — as  most  readers  of  Plato  know,  only  it  is 
a  truth  difficult  to  retain  and  apply — that  what  we  gain  by 
discussing  a  definition  is  often  but  slightly  represented  in 
the  superior  fitness  of  the  formula  that  we  ultimately  adopt; 
it  consists  chiefly  in  the  greater  clearness  and  fulness  in 
which  the  characteristics  of  the  matter  to  which  the 
formula  refers  have  been  brought  before  the  mind  in  the 
process  of  seeking  for  it.  While  we  are  apparently  aiming 
at  definitions  of  terms,  our  attention  should  be  really  fixed 
on  distinctions  and  relations  of  fact.  These  latter  are  what 
we  are  concerned  to  know,  contemplate,  and  as  far  as 
possible  arrange  and  systematise ;  and  in  subjects  where 
we  cannot  present  them  to  the  mind  in  ordinary  fulness  by 
the  exercise  of  the  organs  of  sense,  there  is  no  way  of 
surveying  them  so  convenient  as  that  of  reflecting  on  our 
use  of  common  terms.  ...  In  comparing  different  definitions 
our  aim  should  be  far  less  to  decide  which  we  ought  to 
adopt,  than  to  apprehend  and  duly  consider  the  grounds  on 
which  each  has  commended  itself  to  reflective  minds.  We 
shall  generally  find  that  each  writer  has  noted  some 
relation,  some  resemblance  or  difference,  which  others  have 
overlooked ;  and  we  shall  gain  in  completeness,  and  often 


Verification  of  Meaning.  91 

in  precision,  of  view  by  following  him  in  his  observations, 
whether  or  not  we  follow  him  in  his  conclusions." 1 

Mr.  Sidgwick's  own  discussions  of  Wealth,  Value, 
and  Money  are  models.  A  clue  is  often  found  to  the 
meaning  in  examining  startlingly  discrepant  state 
ments  connected  with  the  same  leading  word.  Thus 
we  find  some  authorities  declaring  that  "  style"  cannot 
be  taught  or  learnt,  while  others  declare  that  it  can. 
But  on  trying  to  ascertain  what  they  mean  by  "  style," 
we  find  that  those  who  say  it  cannot  be  taught  mean 
either  a  certain  marked  individual  character  or  manner 
of  writing — as  in  Buffon's  saying,  Le  style  c'est  Vhomme 
meme — or  a  certain  felicity  and  dignity  of  expression, 
while  those  who  say  style  can  be  taught  mean  lucid 
method  in  the  structure  of  sentences  or  in  the  arrange- 
ment of  a  discourse.  Again  in  discussions  on  the 
rank  of  poets,  we  find  different  conceptions  of  what 
constitutes  greatness  in  poetry  lying  at  the  root  of 
the  inclusion  of  this  or  the  other  poet  among  great 
poets.  We  find  one  poet  excluded  from  the  first  rank 
of  greatness  because  his  poetry  was  not  serious ; 
another  because  his  poetry  was  not  widely  popular ; 
another  because  he  wrote  comparatively  little;  another 
because  he  wrote  only  songs  or  odes  and  never 
attempted  drama  or  epic.  These  various  opinions 
point  to  different  conceptions  of  what  constitutes 
greatness  in  poets,  different  connotations  of  "  great 
poet ".  Comparing  different  opinions  concerning 
"  education  "  we  may  be  led  to  ask  whether  it  means 
more  than  instruction  in  the  details  of  certain  subjects, 
whether  it  does  not  also  import  the  formation  of  a 

1  Sidgwick's  Political  Economy,  pp.  52-3.     Ed.  1883. 


92  Definition. 

disposition    to    learn   or   an    interest   in   learning    or 
instruction  in  a  certain  method  of  learning. 

Historically,  dialectic  turning  on  the  use  of  words 
preceded  the  attempt  to  formulate  principles  of  Defini- 
tion, and  attempts  at  precise  definition  led  to  Division 
and  Classification,  that  is  to  systematic  arrangement 
of  the  objects  to  be  defined.  Attempt  to  define  any 
such  word  as  "  education,"  and  you  gradually  become 
sensible  of  the  needs  in  respect  of  method  that  forced 
themselves  upon  mankind  in  the  history  of  thought. 
You  soon  become  aware  that  you  cannot  define  it  by 
itself  alone  ;  that  you  are  beset  by  a  swarm  of  more  or 
less  synonymous  words,  instruction,  discipline,  culture, 
training,  and  so  on  ;  that  these  various  words  represent 
distinctions  and  relations  among  things  more  or  less 
allied ;  and  that,  if  each  must  be  fixed  to  a  definite 
meaning,  this  must  be  done  with  reference  to  one 
another  and  to  the  whole  department  of  things  that 
they  cover. 

The  first  memorable  attempts  at  scientific  arrange- 
ment were  Aristotle's  treatises  on  Ethics  and  Politics, 
which  had  been  the  subjects  of  active  dialectic 
for  at  least  a  century  before.  That  these  the  most 
difficult  of  all  departments  to  subject  to  scientific 
treatment  should  have  been  the  first  chosen  was  due 
simply  to  their  preponderating  interest :  "  The  proper 
study  of  mankind  is  man  ".  The  systems  of  what  are 
known  as  the  Natural  Sciences  are  of  modern  origin  : 
the  first,  that  of  Botany,  dates  from  Cesalpinus  in 
the  sixteenth  century.  But  the  principles  on  which 
Aristotle  proceeded  in  dividing  and  defining,  principles 
which  have  gradually  themselves  been  more  precisely 
formulated,  are  principles  applicable  to  all  systematic 


Fixation  of  Meaning.  93 

arrangements  for  purposes  of  orderly  study.  I  give 
them  in  the  precise  formulae  which  they  have  gradually 
assumed  in  the  tradition  of  Logic.  The  principles  of 
Division  are  often  given  in  Formal  Logic,  and  the 
principles  of  Classification  in  Inductive  Logic,  but 
there  is  no  valid  reason  for  the  separation.  The 
classification  of  objects  in  the  Natural  Sciences,  of 
animals,  plants,  and  stones,  with  a  view  to  the  thorough 
study  of  them  in  form,  structure,  and  function,  is  more 
complex  than  classifications  for  more  limited  purposes, 
and  the  tendency  is  to  restrict  the  word  classification  to 
these  elaborate  systems.  But  really  they  are  only  a 
series  of  divisions  and  subdivisions,  and  the  same 
principles  apply  to  each  of  the  subordinate  divisions 
as  well  as  to  the  division  of  the  whole  department 
of  study. 

II. — PRINCIPLES  OF  DIVISION  OR  CLASSIFICATION  AND 
DEFINITION. 

Confusion  in  the  boundaries  of  names  arises  from 
confused  ideas  regarding  the  resemblances  and 
differences  of  things.  As  a  protective  against  this 
confusion,  things  must  be  clearly  distinguished  in 
their  points  of  likeness  and  difference,  and  this 
leads  to  their  arrangement  in  systems,  that  is,  to 
division  and  classification.  A  name  is  not  secure 
against  variation  until  it  has  a  distinct  place  in 
such  a  system  as  a  symbol  for  clearly  distinguished 
attributes.  Nor  must  we  forget,  further,  that  systems 
have  their  day,  that  the  best  system  attainable  is 
only  temporary,  and  may  have  to  be  recast  to 
correspond  with  changes  of  things  and  of  man's 
way  of  looking  at  them. 


94  Definition. 

The  leading  principles  of  Division  may  be  stated 
as  follows : — 

I.  Every  division  is  made  on  the  ground  of  differences 

in  some  attribute  common  to  all  the  members  of 
the  whole  to  be  divided. 

This  is  merely  a  way  of  stating  what  a  logical 
division  is.  It  is  a  division  of  a  generic  whole  or 
genus,  an  indefinite  number  of  objects  thought  of 
together  as  possessing  some  common  character  or 
attribute.  All  have  this  attribute,  which  is  technically 
called  the  fundamentum  divisionis,  or  generic  attribute. 
But  the  whole  is  divisible  into  smaller  groups  (species), 
each  of  which  possesses  the  common  character  with 
a  difference  (differentia).  Thus,  mankind  may  be 
divided  into  White  men,  Black  men,  Yellow  men,  on 
ground  of  the  differences  in  the  colour  of  their  skins  : 
all  have  skins  of  some  colour:  this  is  the  fundamentum 
divisionis:  but  each  subdivision  or  species  has  a 
different  colour :  this  is  the  differentia.  Rectilineal 
figures  are  divided  into  triangles,  quadrangles, 
pentagons,  etc.,  on  the  ground  of  differences  in  the 
number  of  angles. 

Unless  there  is  a  fund,  div,,  i.e.,  unless  the  differences 
are  differences  in  a  common  character,  the  division  is 
not  a  logical  division.  To  divide  men  into  Europeans, 
opticians,  tailors,  blondes,  brunettes,  and  dyspeptics 
is  not  to  make  a  logical  division.  This  is  seen  more 
clearly  in  connexion  with  the  second  condition  of  a 
perfect  division. 

II.  In  a  perfect  division,  the  subdivisions  or  species 

are  mutually  exclusive. 

Every   object    possessing    the    common    character 


Fixation  of  Hfeaning,  95 

should  be  in  one  or  other  of  the  groups,  and  none 
should  be  in  more  than  one. 

Confusion  between  classes,  or  overlapping,  may 
arise  from  two  causes.  It  may  be  due  (i)  to  faulty 
division,  to  want  of  unity  in  \hefundamentum  divisionis  ; 
(2)  to  the  indistinct  character  of  the  objects  to  be 
defined. 

(1)  Unless  the  division  is  based  upon  a  single  ground, 
unless  each  species  is  based  upon  some  mode  of  the 
generic  character,  confusion  is  almost  certain  to  arise. 
Suppose   the   field  to  be  divided,  the   objects   to   be 
classified,    are    three-sided    rectilineal    plane    figures, 
each  group  must  be  based  upon  some  modification  of 
the  three  sides.     Divide  them  into  equilateral,  isosceles, 
and   scalene  according  as  the  three   sides  are  all   of 
equal    length,    or   two    of    equal    length,    or   each    of 
different   length,    and    you    have    a    perfect    division. 
Similarly  you  can  divide  them  perfectly  according  to 
the  character  of  the  angles  into  acute-angled,  right- 
angled   and  obtuse-angled.     But  if  you  do  not  keep 
to  a  single  basis,  as  in  dividing  them  into  equilateral, 
isosceles,  scalene,  and  right-angled,  you  have  a  cross- 
division.      The   same  triangle  might    be    both    right- 
angled  and  isosceles. 

(2)  Overlapping,  however,  may  be   unavoidable    in 
practice  owing  to  the   nature  of  the  objects.     There 
may    be    objects    in    which    the    dividing    characters 
are   not  distinctly  marked,    objects   that   possess   the 
differentiae  of  more  than  one  group  in  a  greater  or  less 
degree.     Things  are  not  always  marked  off  from  one 
another   by  hard    and    fast    lines.      They  shade   into 
one   another   by  imperceptible    gradations.      A   clear 
separation  of  them  may  be  impossible.     In  that  case 
you  must  allow  a  certain  indeterminate  margin  between 


96  Definition. 

your  classes,  and  sometimes  it  may  be  necessary  to 
put  an  object  into  more  than  one  class. 

To  insist  that  there  is  no  essential  difference  unless 
a  clear  demarcation  can  be  made  is  a  fallacy.  A 
sophistical  trick  called  the  Sorites  or  Heap  from  the 
classical  example  of  it  was  based  upon  this  difficulty 
of  drawing  sharp  lines  of  definition.  Assuming  that 
it  is  possible  to  say  how  many  stones  constitute  a 
heap,  you  begin  by  asking  whether  three  stones  form 
a  heap.  If  your  respondent  says  No,  you  ask  whether 
four  stones  form  a  heap,  then  five,  and  so  on  and  he 
is  puzzled  to  say  when  the  addition  of  a  single  stone 
makes  that  a  heap  which  was  not  a  heap  befoie.  Or 
you  may  begin  by  asking  whether  twenty  stor.es  form 
a  heap,  then  nineteen,  then  eighteen,  and  so  on,  the 
difficulty  being  to  say  when  what  was  a  heap  ceases 
to  be  so. 

Where  the  objects  classified  are  mixed  states  or 
affections,  the  products  of  interacting  factors,  or 
differently  interlaced  or  interfused  growths  from 
common  roots,  as  in  the  case  of  virtues,  or  emotions, 
or  literary  qualities,  sharp  demarcations  are  impossible. 
To  distinguish  between  wit  and  humour,  or  humour 
and  pathos,  or  pathos  and  sublimity  is  difficult  because 
the  same  composition  may  partake  of  more  than  one 
character.  The  specific  characters  cannot  be  made 
rigidly  exclusive  one  of  another. 

Even  in  the  natural  sciences,  where  the  individuals 
are  concrete  objects  of  perception,  it  may  be  difficult 
to  decide  in  which  of  two  opposed  groups  an  object 
should  be  included.  Sydney  Smith  has  commemorated 
the  perplexities  of  Naturalists  over  the  newly  dis- 
covered animals  and  plants  of  Botany  Bay,  in  especial 
with  the  Ornithorynchus,— "  a  quadruped  as  big  as  a 


Fixation  of  Meaning.  97 

large  cat,  with  the  eyes,  colour,  and  skin  of  a  mole, 
and  the  bill  and  web-feet  of  a  duck — puzzling  Dr. 
Shaw,  and  rendering  the  latter  half  of  his  life  miser- 
able, from  his  utter  inability  to  determine  whether  it 
was  a  bird  or  a  beast". 

III.  The  classes  in  any  scheme  of  division  should 
be  of  co-ordinate  rank. 

The  classes  may  be  mutually  exclusive,  and  yet  the 
division  imperfect,  owing  to  their  not  being  of  equal 
rank.  Thus  in  the  ordinary  division  of  the  Parts  of 
Speech,  parts,  that  is,  of  a  sentence,  Prepositions  and 
Conjunctions  are  not  co-ordinate  in  respect  of  function, 
which  is  the  basis  of  the  division,  with  Nouns,  Adjec- 
tives, Verbs,  and  Adverbs.  The  preposition  is  a  part 
of  a  phrase  which  serves  the  same  function  as  an 
adjective,  e.g.,  royal  army,  army  of  the  king;  it  is  thus 
functionally  part  of  a  part,  or  a  particle.  So  with  the 
conjunction  :  it  also  is  part  of  a  part,  i.e.,  part  of  a 
clause  serving  the  function  of  adjective  or  adverb. 

IV.  The  basis  of  division  (fundamentum  divisionis] 
should  be  an  attribute  admitting  of  important 
differences. 

The  importance  of  the  attribute  chosen  as  basis  may 
vary  with  the  purpose  of  the  division.  An  attribute 
that  is  of  no  importance  in  one  division,  may  be 
important  enough  to  be  the  basis  of  another  division. 
Thus  in  a  division  of  houses  according  to  their  archi- 
tectural attributes,  the  number  of  windows  or  the  rent 
is  of  little  importance ;  but  if  houses  are  taxed  or  rated 
according  to  the  number  of  windows  or  the  rent,  these 
attributes  become  important  enough  to  be  a  basis  of 
division  for  purposes  of  taxation  or  rating.  They  then 
admit  of  important  differences. 

7 


98  Definition. 

That  the  importance  is  relative  to  the  purpose  of  the 
division  should  be  borne  in  mind  because  there  is  a 
tendency  to  regard  attributes  that  are  of  importance 
in  any  familiar  or  pre-eminent  division  as  if  they  had 
an  absolute  importance.  In  short,  disregard  of  this 
relativity  is  a  fallacy  to  be  guarded  against. 

In  the  sciences,  the  purpose  being  the  attainment 
and  preservation  of  knowledge,  the  objects  of  study  are 
divided  so  as  to  serve  that  purpose.  Groups  must  be 
formed  so  as  to  bring  together  the  objects  that  have 
most  in  common.  The  question,  Who  are  to  be  placed 
together  ?  in  any  arrangement  for  purposes  of  study, 
receives  the  same  answer  for  individuals  and  for  classes 
that  have  to  be  grouped  into  higher  classes,  namely, 
Those  that  have  most  in  common.  This  is  what  Dr. 
Bain  happily  calls  "the  golden  rule"  of  scientific 
classification  :  "  Of  the  various  groupings  of  resembling 
things,  preference  is  given  to  such  as  have  the  greatest 
number  of  attributes  in  common  ".  I  slightly  modify 
Dr.  Bain's  statement :  he  says  "  the  most  numerous 
and  the  most  important  attributes  in  common  ".  But 
for  scientific  purposes  number  of  attributes  constitutes 
importance,  as  is  well  recognised  by  Dr.  Fowler  when 
he  says  that  the  test  of  importance  in  an  attribute  pro- 
posed as  a  basis  of  classification  is  the  number  of 
other  attributes  of  which  it  is  an  index  or  invariable 
accompaniment.  Thus  in  Zoology  the  squirrel,  the 
rat,  and  the  beaver  are  classed  together  as  Rodents, 
the  difference  between  their  teeth  and  the  teeth  of 
other  Mammalia  being  the  basis  of  division,  because 
the  difference  in  teeth  is  accompanied  by  differences  in 
many  other  properties.  So  the  hedge-hog,  the  shrew- 
mouse,  and  the  mole,  though  very  unlike  in  outward 
appearance  and  habits,  are  classed  together  as  Insec- 


Fixation  of  Meaning.  99 

tivora,   the    difference   in   what   they   feed   on   being 
accompanied  by  a  number  of  other  differences. 

The  Principles  <?/ Definition.  The  word  "  definition  " 
as  used  in  Logic  shows  the  usual  tendency  of  words  to 
wander  from  a  strict  meaning  and  become  ambiguous. 
Throughout  most  of  its  uses  it  retains  this  much  of  a 
common  signification,  the  fixing  or  determining  of  the 
boundaries  of  a  class1  by  making  clear  its  constituent 
attributes.  Now  in  this  making  clear  two  processes 
may  be  distinguished,  a  material  process  and  a  verbal 
process.  We  have  (i)  the  clearing  up  of  the  common 
attributes  by  a  careful  examination  of  the  objects 
included  in  the  class :  and  we  have  (2)  the  statement 
of  these  common  attributes  in  language.  The  rules 
of  definition  given  by  Dr.  Bain,  who  devotes  a 
separate  Book  in  his  Logic  to  the  subject  of 
Definition,  concern  the  first  of  these  processes :  the 
rules  more  commonly  given  concern  mainly  the 
second. 

One  eminent  merit  in  Dr.  Bain's  treatment  is  that 
it  recognises  the  close  connexion  between  Definition 
and  Classification.  His  cardinal  rules  are  reduced  to 
two. 


1  Some  logicians,  however,  speak  of  defining  a  thing,  and 
illustrate  this  as  if  by  a  thing  they  meant  a  concrete  individual, 
the  realistic  treatment  of  Universals  lending  itself  to  such 
expressions.  But  though  the  authority  of  Aristotle  might  be 
claimed  for  this,  it  is  better  to  confine  the  name  in  strictness  to 
the  main  process  of  defining  a  class.  Since,  however,  the  method 
is  the  same  whether  it  is  an  individual  or  a  class  that  we  want  to 
make  distinct,  there  is  no  harm  in  the  extension  of  the  word 
definition  to  both  varieties.  See  Davidson's  Logic  of  Definition, 
chap.  ii. 


too  Definition. 

I.  Assemble  for  comparison  representative  individuals 

of  the  class. 

II.  Assemble  for  comparison  representative  individuals 

of  the  contrasted  class  or  classes. 

Seeing  that  the  contrasted  classes  are  contrasted  on 
some  basis  of  division,  this  is  in  effect  to  recognise 
that  you  cannot  clearly  define  any  class  except  in  a 
scheme  of  classification.  You  must  have  a  wide  genus 
with  its  fundamentum  divisionis^  and,  within  this,  species 
distinguished  by  their  several  differentia. 

Next,  as  to  the  verbal  process,  rules  are  commonly 
laid  down  mostly  of  a  trifling  and  obvious  character. 
That  "  a  definition  should  state  neither  more  nor  less 
than  the  common  attributes  of  the  class,"  or  than  the 
attributes  signified  by  the  class-name,  is  sometimes 
given  as  a  rule  of  definition.  This  is  really  an 
explanation  of  what  a  definition  is,  a  definition  of  a 
definition.  And  as  far  as  mere  statement  goes  it  is 
not  strictly  accurate,  for  when  the  attributes  of  a 
genus  are  known  it  is  not  necessary  to  give  all  the 
attributes  of  the  species,  which  include  the  generic 
attributes  as  well,  but  it  is  sufficient  to  give  the 
generic  name  and  the  differentia.  Thus  Poetry  may 
be  defined  as  "a  Fine  Art  having  metrical  language 
as  its  instrument".  This  is  technically  known  as 
definition  per  genus  et  differentiam.  This  mode  of 
statement  is  a  recognition  of  the  connexion  between 
Definition  and  Division. 

The  rule  that  "  a  definition  should  not  be  a  synony- 
mous repetition  of  the  name  of  the  class  to  be  defined," 
is  too  obvious  to  require  formal  statement.  To  describe 
a  Viceroy  as  a  man  who  exercises  viceregal  functions, 
may  have  point  as  an  epigram  in  the  case  of  a  faineant 
viceroy,  but  it  is  not  a  definition. 


Fixation  of  Meaning.  101 

So  with  the  rule  that  "  a  definition  should  not  be 
couched  in  ambiguous  unfamiliar,  or  figurative 
language".  To  call  the  camel  "the  ship  of  the 
desert"  is  a  suggestive  and  luminous  description  of 
a.  property,  but  it  is  not  a  definition.  So  with  the 
noble  description  of  Faith  as  "the  substance  of 
things  hoped  for,  the  evidence  of  things  not  seen ". 
But  if  one  wonders  why  so  obvious  a  "rule"  should 
be  laid  down,  the  answer  is  that  it  has  its  historical 
origin  in  the  caprices  of  two  classes  of  offenders, 
mystical  philosophers  and  pompous  lexicographers.1 

That  "the  definition  should  be  simply  convertible 
with  the  term  for  the  class  defined,"  so  that  we  may 
say,  for  example,  either:  "Wine  is  the  juice  of  the 
grape,"  or,  "  The  juice  of  the  grape  is  wine,"  is  an 
obvious  corollary  from  the  nature  of  definition,  but 
should  hardly  be  dignified  with  the  name  of  a  "  rule  ". 

The  Principles  of  Naming.  Rules  have  been  formu- 
lated for  the  choice  of  names  in  scientific  definition  and 
classification,  but  it  may  be  doubted  whether  such  choice 
can  be  reduced  to  precise  rule.  It  is  enough  to  draw 
attention  to  certain  considerations  obvious  enough  on 
reflection. 

We  may  take  for  granted  that  there  should  be 
distinct  names  for  every  defining  attribute  (a  Termi- 
nology] and  for  every  group  or  class  (a  Nomenclature], 
What  about  the  selection  of  the  names  ?  Suppose  an 
investigator  is  struck  with  likenesses  and  differences 
that  seem  to  him  important  enough  to  be  the  basis  of 
a  new  division,  how  should  he  be  guided  in  his  choice 
of  names  for  the  new  groups  that  he  proposes  ?  Should 

1  See  Davidson's  Logic  of  Definition,  chap.  iii. 


102  Definition. 

he  coin  new  names,  or  should  he  take  old  names  and 
try  to  fit  them  with  new  definitions  ? 

The  balance  of  advantages  is  probably  in  favour  of 
Dr.  Whewell's  dictum  that  "  in  framing  scientific 
terms,  the  appropriation  of  old  words  is  preferable  to 
the  invention  of  new  ones".  Only  care  must  be  taken 
to  keep  as  close  as  possible  to  the  current  meaning  of 
•the  old  word,  and  not  to  run  counter  to  strong  associa- 
tions. This  is  an  obvious  precept  with  a  view  to 
avoiding  confusion.  Suppose,  for  example,  that  in 
dividing  Governments  you  take  the  distribution  of 
political  power  as  your  basis  of  division  and  come  to 
the  conclusion  that  the  most  important  differences  are 
whether  this  power  is  vested  in  a  few  or  in  the 
majority  of  the  community.  You  want  names  to  fix 
this  broad  division.  You  decide  instead  of  coining 
the  new  word  Pottarchy  to  express  the  opposite  of 
Oligarchy  to  use  the  old  words  Republic  and  Oligarchy. 
You  would  find,  as  Sir  George  Cornewall  Lewis 
found,  that  however  carefully  you  defined  the  word 
Republic,  a  division  under  which  the  British  Govern- 
ment had  to  be  ranked  among  Republics  would  not 
be  generally  understood  and  accepted.  Using  the 
word  in  the  sense  explained  above,  Mr.  Bagehot 
maintained  that  the  constitution  of  Great  Britain 
was  more  Republican  than  that  of  the  United 
States,  but  his  meaning  was  not  taken  except  by 
a  few. 

The  difficulty  in  choosing  between  new  words  and 
old  words  to  express  new  meanings  is  hardly  felt  in 
the  exact  sciences.  It  is  at  least  at  a  minimum. 
The  innovator  may  encounter  violent  prejudice,  but, 
arguing  with  experts,  he  can  at  least  make  sure  of 
being  understood,  if  his  new  division  is  based  upon 


Fixation  of  Meaning.  103 

real  and  important  differences.     But  in  other  subjects 
the  difficulty  of  transmitting  truth  or  of  expressing  it 
in  language  suited  for  precise  transmission,  is  almost 
greater  than  the  difficulty  of  arriving  at  truth .    Between 
new  names  and  old  names  redefined,  the  possessor  of 
fresh  knowledge,  assuming  it  to  be  perfectly  verified, 
is  in  a  quandary.     The  objects  with  which  he  deals 
are  already  named  in  accordance  with  loose  divisions 
resting  on  strong  prejudices.     The  names  in  current 
use  are  absolutely  incapable  of  conveying  his  meaning. 
He  must  redefine  them  if  he  is  to  use  them.     But  in 
that   case  he  runs   the   risk  of  being  misunderstood 
from  people  being  too  impatient  to  master  his  rede- 
finition.   His  right  to  redefine  may  even  be  challenged 
without  any  reference  to  the  facts  to  be  expressed :  he 
may  simply  be  accused  of  circulating  false  linguistic 
coin,  of  debasing   the   verbal    currency.      The   other 
alternative   open  to  him  is  to  coin  new  words.      In 
that  case  he  runs  the  risk  of  not  being  read  at  all. 
His  contribution  to  verified   knowledge  is  passed  by 
as  pedantic  and  unintelligible.     There  is  no  simple 
rule   of  safety :    between    Scylla   and    Charybdis   the 
mariner  must  steer  as  best  he  may.     Practically  the 
advantage    lies   with    old    words    redefined,    because 
thereby  discussion  is  provoked  and  discussion  clears 
the  air. 

Whether  it  is  best  to  attempt  a  formal  definition 
or  to  use  words  in  a  private,  peculiar,  or  esoteric 
sense,  and  leave  this  to  be  gathered  by  the  reader 
from  the  general  tenor  of  your  utterances,  is  a  question 
of  policy  outside  the  limits  of  Logic.  It  is  for  the 
logician  to  expound  the  method  of  Definition  and  the 
conditions  of  its  application :  how  far  there  are  subjects 
that  do  not  admit  of  its  application  profitably  must  be 


iO4  Definition. 

decided  on  other  grounds.  But  it  is  probably  true 
that  no  man  who  declines  to  be  bound  by  a  formal 
definition  of  his  terms  is  capable  of  carrying  them 
in  a  clear  unambiguous  sense  through  a  heated 
controversy. 


CHAPTER  II. 

THE  FIVE  PREDICABLES.— VERBAL  AND  REAL 
PREDICATION. 

WE  give  a  separate  chapter  to  this  topic  out  of  respect 
for  the  space  that  it  occupies  in  the  history  of  Logic. 
But  except  as  an  exercise  in  subtle  distinction  for  its 
own  sake,  all  that  falls  to  be  said  about  the  Predicables 
might  be  given  as  a  simple  appendix  to  the  chapter  on 
Definition. 

Primarily,  the  Five  Predicables  or  Heads  of  Predi- 
cables— Genus,  Species,  Differentia,  Proprium,  and 
Accidens — are  not  predicables  at  all,  but  merely  a  list 
or  enumeration  of  terms  used  in  dividing  and  defining 
on  the  basis  of  attributes.  They  have  no  meaning 
except  in  connexion  with  a  fixed  scheme  of  division. 
Given  such  a  scheme,  and  we  can  distinguish  in  it 
the  whole  to  be  divided  (the  genus),  the  subordinate 
divisions  (the  species],  the  attribute  or  combination  of 
attributes  on  which  each  species  is  constituted  (the 
differentia),  and  other  attributes,  which  belong  to  some 
or  all  of  the  individuals  but  are  not  reckoned  for  pur- 
poses of  division  and  definition  (Propria  and  Accidentici). 
The  list  is  not  itself  a  logical  division  :  it  is  hetero- 
geneous, not  homogeneous ;  the  two  first  are  names 
of  classes,  the  three  last  of  attributes.  But  correspond- 
ing to  it  we  might  make  a  homogeneous  division  of 
attributes,  as  follows  :  — 


io6  Definition. 

Attributes 


Defining                         Non-defining 

I                       I 

%  Generic 

Specific             Proprium 
(Differentia) 

Accidens 

The  origin  of  the  title  Predicables  as  applied  to  these 
five  terms  is  curious,  and  may  be  worth  noting  as  an 
instance  of  the  difficulty  of  keeping  names  precise,  and 
of  the  confusion  arising  from  forgetting  the  purpose 
of  a  name.  Porphyry  in  his  cto-aywy^  or  Introduction 
explains  the  five  words  (<^cov<u)  simply  as  terms  that  it  is 
useful  for  various  purposes  to  know,  expressly  mention- 
ing definition  and  division.  But  he  casually  remarks 
that  Singular  names,  "This  man,"  "Socrates,"  can 
be  predicated  only  of  one  individual,  whereas  Genera^ 
Species,  Differentia,  etc.,  are  predicable  of  many.  That 
is  to  say  he  describes  them  as  Predicables  simply  by 
contradistinction  from  Singular  names.  A  name, 
however,  was  wanted  for  the  five  terms  taken  all 
together,  and  since  they  are  not  a  logical  division,  but 
merely  a  list  of  terms  used  in  dividing  and  defining, 
there  was  no  apt  general  designation  for  them  such 
as  would  occur  spontaneously.  Thus  it  became  the 
custom  to  refer  to  them  as  the  Predicables,  a  means  of 
reference  to  them  collectively  being  desiderated,  while 
the  meaning  of  this  descriptive  title  was  forgotten. 

To  call  the  five  divisional  elements  or  Divisoria 
Predicables  is  to  present  them  as  a  division  of  Predi- 
cate Terms  on  the  basis  of  their  relation  to  the  Subject 
Term  :  to  suggest  that  every  Predicate  Term  must  be 
either  a  Genus  or  a  Species,  or  a  Differentia,  or  a 


The  Five  Predicates.  107 

Proprium,  or  an  Accidens  of  the  Subject  Term.  They 
are  sometimes  criticised  as  such,  and  it  is  rightly 
pointed  out  that  the  Predicate  is  never  a  species  of  or 
with  reference  to  the  Subject.  But,  in  truth,  the  five 
so-called  Predicables  were  never  meant  as  a  division  of 
predicates  in  relation  to  the  subject :  it  is  only  the  title 
that  makes  this  misleading  suggestion. 

To  complete  the  confusion  it  so  happens  that  Aris- 
totle used  three  of  the  Five  terms  in  what  was  virtually 
a  division  of  Predicates  inasmuch  as  it  was  a  division 
of  Problems  or  Questions.  In  expounding  the  methods 
of  Dialectic  in  the  Topica  he  divided  Problems  into 
four  classes  according  to  the  relation  of  the  Predicate 
to  the  Subject.  The  Predicate  must  either  be  simply 
convertible  with  the  subject  or  not.  If  simply  con- 
vertible, the  two  must  be  coextensive,  and  the  Predi- 
cate must  be  either  a  Proprium  or  the  Definition.  If 
not  simply  convertible,  the  Predicate  must  either  be 
part  of  the  Definition  or  not.  If  part  of  the  Definition 
it  must  be  either  a  Generic  Property  or  a  Differentia 
(both  of  which  in  this  connexion  Aristotle  includes 
under  Genus) :  if  not  part  of  the  Definition,  it  is  an 
Accident.  Aristotle  thus  arrives  at  a  fourfold  division 
of  Problems  or  Predicates : — yo/os  (Genus,  including 
Differentia,  S«x</>opa) ;  6/oos  (Definition) ;  TO  tSiov  (Pro- 
prium] ;  and  TO  o-u/x/iJe/fyKos  (Accidens].  The  object  of  it 
was  to  provide  a  basis  for  his  systematic  exposition ; 
each  of  the  four  kinds  admitted  of  differences  in 
dialectic  method.  For  us  it  is  a  matter  of  simple 
curiosity  and  ingenuity.  It  serves  as  a  monument  of 
how  much  Greek  dialectic  turned  on  Definition,  and  it 
corresponds  exactly  to  the  division  of  attributes  into 
Defining  and  Non-defining  given  above.  It  is  some- 
times said  that  Aristotle  showed  a  more  scientific  mind 


io8  Definition. 

than  Porphyry  in  making  the  Predicables  four  instead 
of  five.  This  is  true  if  Porphyry's  list  had  been  meant 
as  a  division  of  attributes  :  but  it  was  not  so  meant. 

The  distinction  between  Verbal  or  Analytic  and 
Real  or  Synthetic  Predication  corresponds  to  the 
distinction  between  Denning  and  Non-defining  attri- 
butes, and  also  has  no  significance  except  with 
reference  to  some  scheme  of  Division,  scientific  and 
precise  or  loose  and  popular. 

When  a  proposition  predicates  of  a  subject  something 
contained  in  the  full  notion,  concept,  or  definition  of 
the  subject  term,  it  is  called  Verbal,  Analytic,  or 
Explicative :  verbal,  inasmuch  as  it  merely  explains 
the  meaning  of  a  name;  explicative  for  the  same 
reason ;  analytic,  inasmuch  as  it  unties  the  bundle  of 
attributes  held  together  in  the  concept  and  pays  out 
one,  or  all  one  by  one. 

When  the  attributes  of  the  Predicate  are  not  contained 
in  the  concept  of  the  Subject,  the  proposition  is  called 
\Real,  Synthetic,  or  AmpliatfDCjfot  parallel  reasons.  * 

Thus:  "A  triangle  is  a  three-sided  rectilinear 
figure "  is  Verbal  or  Analytic  ;  "  Triangles  have 
three  angles  together  equal  to  two  right  angles," 
or  "Triangles  are  studied  in  schools,"  is  Real  or 
Synthetic. 

According  to  this  distinction,  predications  of  the 
whole  Definition  or  of  a  Generic  attribute  or  of  a 
Specific  attribute  are  Verbal :  predications  of  Accident 
are  Real.  A  nice  point  is  whether  Propria  are  Verbal 
or  Real.  They  can  hardly  be  classed  with  Verbal, 
inasmuch  as  one  may  know  the  full  meaning  of  the 
name  without  knowing  them  :  but  it  might  be  argued 
that  they  are  Analytic,  inasmuch  as  they  are  implicitly 


The  Five  Predicables.  109 

contained  in  the  defining  attributes  as  being  deducible 
from  them. 

Observe,  however,  that  the  whole  distinction  is  really 
valid  only  in  relation  to  some  fixed  or  accepted  scheme 
of  classification  or  division.  Otherwise,  what  is  Verbal 
or  Analytic  to  one  man  may  be  Real  or  Synthetic  to 
another.  It  might  even  be  argued  that  every  proposi- 
tion is  Analytic  to  the  man  who  utters  it  and  Synthetic 
to  the  man  who  receives  it.  We  must  make  some 
analysis  of  a  whole  of  thought  before  paying  it  out  in 
words  :  and  in  the  process  of  apprehending  the  meaning 
of  what  we  hear  or  read  we  must  add  the  other  members 
of  the  sentence  on  to  the  subject.  Whether  or  not  this 
is  super-subtle,  it  clearly  holds  good  that  what  is 
Verbal  (in  the  sense  defined)  to  the  learned  man  of 
science  may  be  Real  to  the  learner.  That  the  horse 
has  six  incisors  in  each  jaw  or  that  the  domestic  dog- 
has  a  curly  tail,  is  a  Verbal  Proposition  to  the  Natural 
Historian,  a  mere  exposition  of  defining  marks ;  but 
the  plain  man  has  a  notion  of  horse  or  dog  into  which 
this  defining  attribute  does  not  enter,  and  to  him 
accordingly  the  proposition  is  Real. 

But  what  of  propositions  that  the  plain  man  would 
at  once  recognise  as  Verbal  ?  Charles  Lamb,  for 
example,  remarks  that  the  statement  that  "a  good 
name  shows,  the  estimation  in  which  a  man  is  held 
in  the  world  "  is  a  verbal  proposition.  Where  is  the 
fixed  scheme  of  division  there  ?  The  answer  is  that 
by  a  fixed  scheme  of  division  we  do  not  necessarily 
mean  a  scheme  that  is  rigidly,  definitely  and  precisely 
fixed.  To  make  such  schemes  is  the  business  of 
Science.  But  the  ordinary  vocabulary  of  common 
intercourse  as  a  matter  of  fact  proceeds  upon  schemes 
of  division,  though  the  names  used  in  common  speech 


no  Definition. 

are  not  always  scientifically  accurate,  not  always  the 
best  that  could  be  devised  for  the  easy  acquisition  and 
sure  transmission  of  thorough  knowledge.  The  plain 
man's  vocabulary,  though  often  twisted  aside  by  such 
causes  as  we  have  specified,  is  roughly  moulded  on 
the  most  marked  distinguishing  attributes  of  things. 
This  was  practically  recognised  by  Aristotle  when  he 
made  one  of  his  modes  of  definition  consist  in  some- 
thing like  what  we  have  called  verifying  the  meaning 
of  a  name,  ascertaining  the  attributes  that  it  signifies 
in  common  speech  or  in  the  speech  of  sensible  men. 
This  is  to  ascertain  the  essence;  overta,  or  Substantia, 
of  things,  the  most  salient  attributes  that  strike  the 
common  eye  either  at  once  or  after  the  closer  inspection 
that  comes  of  long  companionship,  and  form  the  basis 
of  the  ordinary  vocabulary.  "  Properly  speaking," 
Mansel  says,1  "All  Definition  is  an  inquiry  into 
Attributes.  Our  complex  notions  of  Substances  can 
only  be  resolved  into  various  Attributes,  with  the 
addition  of  an  unknown  substratum:  a  something  to 
which  we  are  compelled  to  regard  these  attributes 
as  belonging.  Man^  for  example,  is  analysed  into 
Animality,  Rationality,  and  the  something  which 
exhibits  these  phenomena.  Pursue  the  analysis  and 
the  result  is  the  same.  We  have  a  something 
corporeal,  animated,  sensible,  rational.  An  unknown 
constant  must  always  be  added  to  complete  the 
integration."  This  "unknown  constant"  was  what 
Locke  called  the  Real  Essence,  as  distinguished  from 
the  Nominal  Essence,  or  complex  of  attributes.  It 

1  Aldrich's  Compendium,  Appendix,  Note  C.  The  reader  may 
be  referred  to  Mansel's  Notes  A  and  C  for  valuable  historical 
notices  of  the  Predicables  and  Definition. 


The  Five  Predicates .  in 

is  upon  this  nominal  essence,  upon  divisions  of  things 
according  to  attributes,  that  common  speech  rests, 
and  if  it  involves  many  cross-divisions,  this  is 
because  the  divisions  have  been  made  for  limited 
and  conflicting  purposes. 


CHAPTER  III. 

ARISTOTLE'S   CATEGORIES. 

IN  deference  to  tradition  a  place  must  be  found  in 
every  logical  treatise  for  Aristotle's  Categories.  No 
writing  of  the  same  length  has  exercised  a  tithe  of  its 
influence  on  human  thought.  It  governed  scholastic 
thought  and  expression  for  many  centuries,  being  from 
its  shortness  and  consequent  easiness  of  transcription 
one  of  the  few  books  in  every  educated  man's  library. 
It  still  regulates  the  subdivisions  of  Parts  of  Speech  in 
our  grammars.  Its  universality  of  acceptance  is  shown* 
in  the  fact  that  the  words  category  (/car^yo/ota)  and  pre- 
dicament^ its  Latin  translation,  have  passed  into 
common  speech. 

The  Categories  have  been  much  criticised  and  often 
condemned  as  a  division,  but,  strange  to  say,  few  have 
inquired  what  they  originally  professed  to  be  a  division 
of,  or  what  was  the  original  author's  basis  of  division. 
Whether  the  basis  is  itself  important,  is  another 
question  :  but  to  call  the  division  imperfect,  without 
reference  to  the  author's  intention,  is  merely  confusing, 
and  serves  only  to  illustrate  the  fact  that  the  same 
objects  may  be  differently  divided  on  different  principles 
of  division.  Ramus  was  right  in  saying  that  the 
Categories  had  no  logical  significance,  inasmuch  as 

(112) 


Aristotle  's  Categories.  ,      113 

they  could  not  be  made  a  basis  for  departments  of 
logical  method  ;  and  Kant  and  Mill  in  saying  that  they 
had  no  philosophical  significance,  inasmuch  as  they  are 
founded  upon  no  theory  of  Knowing  and  Being  :  but 
this  is  to  condemn  them  for  not  being  what  they  were 
never  intended  to  be. 

The  sentence  in  which  Aristotle  states  the  objects  to 
be  divided,  and  his  division  of  them  is  so  brief  and  bold 
that  bearing  in  mind  the  subsequent  history  of  the 
Categories,  one  first  comes  upon  it  with  a  certain 
surprise.  He  says  simply  :— 

"Of  things  expressed  without  syntax  (i.e.,  single 
words),  each  signifies  either  substance,  or  quantity,  or 
quality,  or  relation,  or  place,  or  time,  or  disposition 
(i.e.,  attitude  or  internal  arrangement),  or  appurtenance, 
or  action  (doing),  or  suffering  (being  done  to)."  1 

The  objects,  then,  that  Aristotle  proposed  to  classify 
were  single  words  (the  themata  simplicia  of  the  School- 
men). He  explains  that  by  "  out  of  syntax  "  (dvev 
o-vfjLTrXoKrjs)  he  means  without  reference  to  truth  or 
falsehood:  there  can  be  no  declaration  of  truth  or 
falsehood  without  a  sentence,  a  combination,  or  syntax  : 
"man  runs"  is  either  true  or  false,  "man"  by  itself, 
"  runs  "  by  itself,  is  neither.  His  division,  therefore, 
was  a  division  of  single  words  according  to  their  dif- 
ferences of  signification,  and  without  reference  to  the 
truth  or  falsehood  of  their  predication.2 

Signification   was  thus  the  basis  of  division.     But 


1  TU)V    Kara  ^Sefiiav   ffv^TrXoK^v  \eyofj.€voov    fKaffrov  $)TOI  ova-'iav 

t,  %  -jroa-bv,  $  iroibv,  %  irp6s   n,   %  irov,  %   Trore,   %   Ke'iaOai,  -/) 
exeif,  2}  TToteij/,  ^  Tratrxeii'.      (Categ.  ii.  6.) 

2  To   describe   the   Categories    as  a  grammatical  division,  as 
Mansel  does  in  his  instructive  Appendix  C  to  Aldrich,   is  a  little 
misleading  without  a  qualification.     They  are  non-logical  inas- 

8 


ii4  Definition. 

according  to  what  differences  ?  The  Categories  them- 
selves are  so  abstract  that  this  question  might  be 
discussed  on  their  bare  titles  interminably.  But  often 
when  abstract  terms  are  doubtful,  an  author's  intention 
may  be  gathered  from  his  examples.  And  when  Aris- 
totle's examples  are  ranged  in  a  table,  certain  principles 
of  subdivision  leap  to  the  eyes.  Thus  : — 


much  as  they  have  no  bearing  on  any  logical  purpose.     But  they 
are  grammatical  only  in  so  far  as  they  are  concerned  with  words. 
They  are  not  grammatical  in  the  sense  of  being  concerned  with 
the  function  of  words  in  predication.     The  unit  of  grammar  in 
this  sense  is  the  sentence,  a  combination  of  words  in  syntax ;  and 
it  is  expressly  with  words  out  of  syntax  that  Aristotle  deals,  with 
single  words  not  in  relation  to  the  other  parts  of  a  sentence,  but  in 
relation  to  the  things  signified.     In  any  strict  definition  of  the 
provinces   of  Grammar   and   Logic,  the   Categories  are   neither 
grammatical    nor    logical  :    the   grammarians  have  appropriated 
them  for  the  subdivision  of  certain  parts  of  the  sentence,  but  with 
no  more  right  than  the  logicians.     They  really  form  a  treatise  by 
themselves,  which  is  in  the  main  ontological,  a  discussion  of  sub- 
stances and  attributes  as  underlying  the  forms  of  common  speech. 
In  saying  this  I  use  the  word  substance  in  the  modern  sense :  but 
it  must  be  remembered  that  Aristotle's  ovcrta,  translated  substantia, 
covered   the  word  as  well  as   the   thing  signified,  and  that   his 
Categories  are  primarily  classes  of  words.     The  union  between 
names  and  things  would  seem  to  have  been  closer  in  the  Greek 
mind  than  we  can  now  realise.     To  get  at  it  we  must  note  that 
every  separate  word  (rb  Xeyd/Aevov]  is  conceived  as  having  a  being 
or   thing   (rb  ov)    corresponding  to   it,   so  that  beings  or  things 
(TO.  ovra)  are  coextensive  with  single  words  :  a  being  or  thing  is 
whatever  receives    a  separate  name.     This  is   clear  and   simple 
enough,  but  perplexity  begins  when  we  try  to  distinguish  between 
this  nameable  being  and  concrete  being,  which  last  is  Aristotle's 
category  of  ov<rla,  the  being  signified  by  a  Proper  or  a  Common 
as  distinguished  from  an  Abstract  Noun.     As  we  shall  see,  it  is 
relatively  to  the  highest  sense  of  this  last  kind  of  being,  namely, 
the  being  signified  by  a  Proper  name,  that  he  considers  the  other 
kinds  of  being. 


Aristotle's  Categories. 


Substance 

Man                   \  COMMON  f 

(oucrta) 

(av0pct>7ros)             J     NOUN     \ 

(Substantid) 

Quantity 

Five-feet-five    " 

' 

(TTOOTOV) 

(rpLirrjxv) 

(  Quantitas] 

Quality 

Scholarly 

,0 

(TTOIOI/) 

(ypa/x/xartKOv) 

w 
o         ^ 

(Qualitas) 

H 

Relation 

Bigger 

W 

(?rpos  rt) 

(ptl&v) 

(Relatio) 

. 

\ 

Place 

In-the-Lyceum^                   / 

(TTOV) 

(eV  AWa>) 

> 

<  Ubi) 

o 

Time 

Yesterday 

w 

(TTOTt) 

(x^e?) 

n 

(  Quando) 

. 

Disposition 

Reclines 
(a" 

(Positio} 

; 

Appurtenance 

Has-shoes-on 

(Habitus) 

(^oScSerat) 

w 

Action 

Cuts 

dfl 

(Trotetv) 

(re/xvet) 

(Actio) 

Passion 

Is  cut 

(Tracr^etv) 

(re/x,i/€Tat) 

0 
Substance 


Permanent 


Attribute 


Temporary 


Attribute 


In  looking  at  the  examples,  our  first  impression 
is  that  Aristotle  has  fallen  into  a  confusion.  He 
professes  to  classify  words  out  of  syntax,  yet  he 


n6  Definition. 

gives  words  with  the  marks  of  syntax  on  them. 
Thus  his  division  is  accidentally  grammatical,  a 
division  of  parts  of  speech,  parts  of  a  sentence, 
into  Nouns,  Adjectives,  Adverbs,  and  Verbs.  And 
his  subdivisions  of  these  parts  are  still  followed  in 
our  grammars.  But  really  it  is  not  the  grammatical 
function  that  he  attends  to,  but  the  signification : 
and  looking  further  at  the  examples,  we  see  what 
differences  of  signification  he  had  in  his  mind.  It 
is  differences  relative  to  a  concrete  individual, 
differences  in  the  words  applied  to  him  according 
as  they  signify  the  substance  of  him  or  his  attributes, 
permanent  or  temporary.  1^ 

Take  any  concrete  thing,  Socrates,  this  book,  this^  9r 
table.  It  must  be  some  kind  of  a  thing,  a  man,  a 
book.  It  must  have  some  size  or  quantity,  six  feet 
high,  three  inches  broad.  It  must  have  some  quality, 
white,  learned,  hard.  It  must  have  relations  with 
other  things,  half  this,  double  that,  the  son  of  a 
father.  It  must  be  somewhere,  at  some  time,  in 
some  attitude,  with  some  "  havings,"  appendages,, 
appurtenances,  or  belongings,  doing  something,  or 
having  something  done  to  it.  Can  you  conceive  any 
name  (simple  or  composite)  applicable  to  any  object 
of  perception,  whose  signification  does  not  fall  into 
one  or  other  of  these  classes  ?  If  you  cannot,  the 
categories  are  justified  as  an  exhaustive  division  of 
significations.  They  are  a  complete  list  of  the  most 
general  resemblances  among  individual  things,  in 
other  words,  of  the  summa  genera,  the  genera  general- 
issima  of  predicates  concerning  this,  that  or  the 
other  concrete  individual.  No  individual  thing  is 
sui  generis:  everything  is  like  other  things:  the 
categories  are  the  most  general  likenesses. 


Aristotle's  Categories.  117 

The  categories  are  exhaustive,  but  do  they  fulfil 
another  requisite  of  a  good  division — are  they  mutually 
exclusive  ?  Aristotle  himself  raised  this  question,  and 
some  of  his  answers  to  difficulties  are  instructive. 
Particularly  his  discussion  of  the  distinction  between 
Second  Substances  or  Essences  and  Qualities.  Here 
he  approximates  to  the  modern  doctrine  of  the  distinc- 
tion between  Substance  and  Attribute  as  set  forth  in 
our  quotation  from  Mansel  at  p.  no.  Aristotle's 
Second  Essences  (Seirrepai  ovo-tai)  are  common  nouns 
or  general  names,  Species  and  Genera,  man,  horse, 
animal,  as  distinguished  from  Singular  names,  this 
man,  this  horse,  which  he  calls  First  Substances  (Trpwrat 
ovcrtat),  essences  par  excellence,  to  which  real  existence  in 
the  highest  sense  is  attributed.  Common  nouns  are  put 
in  the  First  Category  because  they  are  predicated  in 
answer  to  the  question,  What  is  this  ?  But  he  raises 
the  difficulty  whether  they  may  not  rather  be  regarded 
as  being  in  the  Third  Category,  that  of  Quality  (TO 
-TTOIOV).  When  we  say,  "This  is  a  man,"  do  we  not 
declare  what  sort  of  a  thing  he  is  ?  do  we  not  declare 
his  Quality  ?  If  Aristotle  had  gone  farther  along 
this  line,  he  would  have  arrived  at  the  modern  point 
of  view  that  a  man  is  a  man  in  virtue  of  his  possessing 
certain  attributes,  that  general  names  are  applied  in 
virtue  of  their  connotation.  This  would  have  been 
to  make  the  line  of  distinction  between  the  First 
Category  and  the  Third  pass  between  First  Essence 
and  Second,  ranking  the  Second  Essences  with 
Qualities.  But  Aristotle  did  not  get  out  of  the 
difficulty  in  this  way.  He  solved  it  by  falling  back 
on  the  differences  in  common  speech.  "Man"  does 
not  signify  the  quality  simply,  as  "whiteness"  does. 
•"  Whiteness  "  signifies  nothing  but  the  quality.  That 


1 1 8  Definition. 

is  to  say,  there  is  no  separate  name  in  common 
speech  for  the  common  attributes  of  man.  His 
further  obscure  remark  that  general  names  "  define 
quality  round  essence "  (Trept  oucriav),  inasmuch  as 
I  they  signify  what  sort  a  certain  essence  is,  and  that  ' 
genera  make  this  definition  more  widely  than  species, 
bore  fruit  in  the  mediaeval  discussions  between  Realists 
and  Nominalists  by  which  the  signification  of  general 
names  was  cleared  up. 

Another  difficulty  about  the  mutual  exclusiveness  of 
the  Categories  was  started  by  Aristotle  in  connexion 
with  the  Fourth  Category,  Relation  (Trpos  TL  Adaliquid, 
To  something).  Mill  remarks  that  "  that  could  not  be 
a  very  comprehensive  view  of  the  nature  of  Relation 
which  would  exclude  action,  passivity,  and  local  situation 
from  that  Category,"  and  many  commentators,  from 
Simplicius  down  to  Hamilton,  have  remarked  that  all 
the  last  six  Categories  might  be  included  under  Rela- 
tion. This  is  so  far  correct  that  the  word  Relation  is  one 
of  the  vaguest  and  most  extensive  of  words  ;  but  the 
criticism  ignores  the  strictness  with  which  Aristotle 
confined  himself  in  his  Categories  to  the  forms  of 
common  speech.  It  is  clear  from  his  examples  that  in 
his  Fourth  Category  he  was  thinking  only  of  "  relation  " 
as  definitely  expressed  in  common  speech.  In  his 
meaning,  any  word  is  a  relative  which  is  joined  with 
another  in  a  sentence  by  means  of  a  preposition  or 
a  case-inflection.  Thus  "  disposition  "  is  a  relative : 
it  is  the  disposition  of  something.  This  kind  of 
relation  is  perfect  when  the  related  terms  reciprocate 
grammatically;  thus  "master,"  "servant,"  since  we 
can  say  either  "the  master  of  the  servant,"  or  "the 
servant  of  the  master".  In  mediaeval  logic  the  term 
Relata  was  confined  to  these  perfect  cases,  but  the 


Aristotle's  Categories./  119 

Category  had  a  wider  scope  with  Aristotle.  And  he 
expressly  raised  the  question  whether  a  word  might 
not  have  as  much,  right  to  be  put  in  another  Category 
as  in  this.  Indeed,  he  went  further  than  his  critics 
in  his  suggestions  of  what  Relation  might  be  made 
to  include.  Thus:  "big"  signifies  Quality;  yet  a 
thing  is  big  with  reference  to  something  else,  and  is 
so  far  a  Relative.  Knowledge  must  be  knowledge  of 
something,  and  is  a  relative :  why  then  should  we  put 
"knowing"  (i.e.,  learned)  in  the  Category  of  Quality. 
"  Hope  "  is  a  relative,  as  being  the  hope  of  a  man  and 
the  hope  of  something.  Yet  we  say,  "  I  have  hope," 
and  there  hope  would  be  in  the  category  of  Having, 
Appurtenance.  For  the  solution  of  all  such  difficulties, 
Aristotle  falls  back  upon  the  forms  of  common  speech, 
and  decides  the  place  of  words  in  his  categories 
according  to  them.  This  was  hardly  consistent  with 
his  proposal  to  deal  with  separate  words  out  of  syntax, 
if  by  this  was  meant  anything  more  than  dealing  with 
them  without  reference  to  truth  or  falsehood.  He  did 
not  and  could  not  succeed  in  dealing  with  separate 
words  otherwise  than  as  parts  of  sentences,  owing 
their  signification  to  their  position  as  parts  of  a  transient 
plexus  of  thought.  In  so  far  as  words  have  their  being 
in  common  speech,  and  it  is  their  being  in  this  sense 
that  Aristotle  considers  in  the  Categories,  it  is  a 
transient  being.  What  being  they  represent  besides  is, 
in  the  words  of  Porphyry,  a  very  deep  affair,  and  one 
that  needs  other  and  greater  investigation. 


CHAPTER  IV. 

THE  CONTROVERSY  ABOUT  UNIVERSALS.— DIFFI- 
CULTIES CONCERNING  THE  RELATION  OF 
GENERAL  NAMES  TO  THOUGHT  AND  TO 
REALITY. 

IN  the  opening  sentences  of  his  Isagoge,  before  giving 
his  simple  explanation  of  the  Five  Predicables, 
Porphyry  mentions  certain  questions  concerning 
Genera  and  Species,  which  he  passes  over  as  being 
too  difficult  for  the  beginner.  "  Concerning  genera  and 
species,"  he  says,  "the  question  whether  they  subsist 
(i.e.,  have  real  substance),  or  whether  they  lie  in  the 
mere  thoughts  only,  or  whether,  granting  them  to  sub- 
sist, they  are  corporeal  or  incorporeal,  or  whether  they 
subsist  apart,  or  in  sensible  things  and  cohering  round 
them — this  I  shall  pass  over,  such  a  question  being  a 
very  deep  affair  and  one  that  needs  other  and  greater 
investigation." 

This  passage,  written  about  the  end  of  the  third 
century,  A.D.,  is  a  kind  of  isthmus  between  Greek 
Philosophy  and  Mediaeval :  it  summarises  questions 
which  had  been  turned  over  on  every  side  and  most 
intricately  discussed  by  Plato  and  Aristotle  and  their 
successors,  and  the  bald  summary  became  a  starting- 
point  for  equally  intricate  discussions  among  the 
Schoolmen,  among  whom  every  conceivable  variety  of 
doctrine  found  champions.  The  dispute  became  known 
(120) 


The  Controversy  about  Universal*.  121 

as  the  dispute  about  Univerails,  and  three  ultra- 
typical  forms  of  doctriney^ere  developed,  known 
respectively  as  Realism,  Nominalism,  and  Concep- 
tualism.  Undoubtedly  the  dispute,  with  all  its  waste 
of  ingenuity,  had  a  clearing  effect,  and  we  may  fairly 
try  now  what  Porphyry  shrank  from,  to  gather  some 
simple  results  for  the  better  understanding  of  general 
names  and  their  relations  to  thoughts  and  to  things. 
The  rival  schools  had  each  some  aspect  of  the  general 
name  in  view,  which  their  exaggeration  served  to 
render  more  distinct. 

What  does  a  general  name  signify  ?  For  logical 
purposes  it  is  sufficient  to  answer — the  points  of 
resemblance  as  grasped  in  the  mind,  fixed  by  a  name 
applicable  to  each  of  the  resembling  individuals.  This 
is  the  signification  of  the  general  name  logically,  its 
connotation  or  concept,  the  identical  element  of 
objective  reference  in  all  uses  of  a  general  name. 

But  other  questions  may  be  asked  that  cannot  be  so 
simply  answered.  What  is  this  concept  in  thought  ? 
What  is  there  in  our  minds  corresponding  to  the 
general  name  when  we  utter  it  ?  How  is  its  significa- 
tion conceived  ?  What  is  the  signification  psycho- 
logically ? 

We  may  ask,  further,  What  is  there  in  nature  that 
the  general  name  signifies  ?  What  is  its  relation  to 
reality  ?  What  corresponds  to  it  in  the  real  world  ? 
Has  the  unity  that  it  represents  among  individuals  no 
existence  except  in  the  mind  ?  Calling  this  unity,  this 
one  in  the  many,  the  Universal  (Universale,  TO  TTUV), 
what  is  the  Universal  ontologically  ? 

It  was  this  ontological  question  that  was  so  hotly 
and  bewilderingly  debated  among  the  Schoolmen. 
Before  giving  the  ultra-typical  answers  to  it,  it  may  be 


122  Definition. 

well  to  note  how  this  question  was  mixed  up  with  still 
other  questions  of  Theology  and  Cosmogony.  Recog- 
nising that  there  is  a  unity  signified  by  the  general 
name,  we  may  go  on  to  inquire  into  the  ground  of  the 
unity.  Why  are  things  essentially  like  one  another  ? 
How  is  the  unity  maintained  ?  How  is  it  continued  ? 
Where  does  the  common  pattern  come  from  ?  The 
question  of  the  nature  of  the  Universal  thus  links  itself 
with  metaphysical  theories  of  the  construction  of  the 
world,  or  even  with  the  Darwinian  theory  of  the  origin 
of  species. 

Passing  by  these  remoter  questions,  we   may  give! 
Hhe  answers  of  the  three  extreme  schools  to  the  onto- 
logical  question,  What  is  a  Universal? 

The  answer  of  the  Ultra-Realists,  broadly  put,  was 
that  a  Universal  is  a  substance  having  an  independent 
existence  in  nature. 

Of  the  Ultra-Nominalists,  that  the  Universal  is  a 
name  and  nothing  else,  vox  et  praterea  nihil ;  that 
this  name  is  the  only  unity  among  the  individuals  of 
a  species,  all  that  they  have  in  common. 

Of  the  Ultra-Conceptualists,  that  the  individuals 
have  more  in  common  than  the  name,  that  they  have 
the  name  plus  the  meaning,  vox  +  significatio,  but  that 
the  Universals,  the  genera  and  species,  exist  only  in 
the  mind. 

Now  these  extreme  doctrines,  as  literally  interpreted 
by  opponents,  are  so  easily  refuted  and  so  manifestly 
untenable,  that  it  may  be  doubted  whether  they  were 
ever  held  by  any  thinker,  and  therefore  I  call  them 
Ultra-Realism,  Ultra-Nominalism,  and  Ultra-Concep- 
tualism.  They  are  mere  exaggerations  or  caricatures, 
set  up  by  opponents  because  they  can  be  easily  knocked 
down. 


The  Controversy  about  Universals.  123 

To  the  Ultra-Realists,  it  is  sufficient  to  say  that  if 
there  existed  anywhere  a  substance  having  all  the 
common  attributes  of  a  species  and  only  these,  having 
none  of  the  attributes  peculiar  to  any  of  the  individuals 
of  that  species,  corresponding  to  the  general  name  as 
an  individual  corresponds  to  a  Proper  or  Singular 
name,  it  would  not  be  the  Universal,  the  unity 
pervading  the  individuals,  but  only  another  individual. 

To  the  Ultra-Nominalists,  it  is  sufficient  to  say  that 
the  individuals  must  have  more  in  common  than  the 
name,  because  the  name  is  not  applied  arbitrarily, 
but  on  some  ground.  The  individuals  must  have  in 
common  that  on  account  of  which  they  receive  the 
common  name :  to  call  them  by  the  same  name  is 
not  to  make  them  of  the  same  species. 

To  the  Ultra-Conceptualists,  it  is  sufficient  to  say 
that  when  we  employ  a  general  name,  as  when  we  say 
"  Socrates  is  a  man,"  we  do  not  refer  to  any  passing 
thought  or  state  of  mind,  but  to  certain  attributes 
independent  of  what  is  passing  in  our  minds.  We 
cannot  make  a  thing  of  this  or  that  species  by  merely 
thinking  of  it  as  such. 

The  ultra-forms  of  these  doctrines  are  thus  easily 
shown  to  be  inadequate,  yet  each  of  the  three,  Realism, 
Nominalism,  and  Conceptualism,  represents  a  phase 
of  the  whole  truth. 

Thus,  take  Realism.  Although  it  is  not  true  that 
there  is  anything  in  reality  corresponding  to  the 
general  name  such  as  there  is  corresponding  to  the 
singular  name,  the  general  name  merely  signifying 
attributes  of  what  the  singular  name  signifies,  it 
does  not  follow,  as  the  opponents  of  Ultra-Realism 
hastily  assume,  that  there  is  nothing  in  the  real 
world  corresponding  to  the  general  name.  Three 


124  Definition. 

senses   may   be   particularised    in    which    Realism    is 
justified. 

(1)  The   points   of    resemblance   from    which    the 
concept    is    formed    are    as    real    as   the    individuals 
themselves.      It   is   true   in    a    sense   that   it   is  our 
thought   that    gives   unity   to    the   individuals   of    a 
class,   that   gathers  the    many   into    one,   and   so   far 
the   Conceptualists    are   right.      Still  we    should   not 
gather  them  into  one  if  they  did    not  resemble  one 
another :    that  is  the  reason  why  we  think  of  them 
together :    and  the  respects    in  which   they  resemble 
one   another   are   as    much    independent   of    us   and 
our  thinking  as  the  individuals  themselves,  as  much 
beyond  the   power   of  our   thought  to  change.     We 
must  go  behind  the  activity  of  the  mind  in  unifying 
to  the  reason  for  the  unification  :  and  the  ground  of  * 
unity  is  found   in   what   really  exists.      We   do    not 
confer  the  unity :    we  do    not   make  all   men   or  all 
dogs  alike :  we  find  them  so.     The   curly  tails  in  a 
thousand  domestic  dogs,  which    serve  to  distinguish 
them    from    wolves    and    foxes,    are    as   real    as    the 
thousand    individual    domestic  dogs.      In   this    sense 
the  Aristotelian  doctrine,   Universalia  in  re,  expresses 

a  plain  truth. 

(2)  The  Platonic  doctrine,  formulated  by  the  School- 
men as  Universalia  ante  rem,  has  also  a  plain  validity. 
Individuals  come  and  go,  but  the  type,  the  Universal, 
is  more  abiding.     Men  are  born  and  die  :  man  remains 
throughout.     The  snows  of  last  year  have  vanished, 
but  snow  is  still  a  reality  to  be  faced.     Wisdom  does 
not  perish  with  the  wise  men  of  any  generation.     In 
this  plain  sense,  at  least,  it  is  true  that  Universals  exist 
before  Individuals,  have  a  greater  permanence,  or,  if  we 
like  to  say  so,  a  higher,  as  it  is  a  more  enduring,  reality. 


The  Controversy  about  Universais.  125 

(3)  Further,  the  "idea,"  concept,  or  universal, 
though  it  cannot  be  separated  from  the  individual, 
and  whether  or  not  we  ascribe  to  it  the  separate 
suprasensual  existence  of  the  archetypal  forms  of 
Plato's  poetical  fancy,  is  a  very  potent  factor  in  the 
real  world.  Ideals  of  conduct,  of  manners,  of  art,  of 
policy,  have  a  traditional  life :  they  do  not  pass  away 
with  the  individuals  in  whom  they  have  existed,  in 
whom  they  are  temporarily  materialised :  they  survive 
as  potent  influences  from  age  to  age.  The  "  idea"  of 
Chaucer's  Man  of  Law,  who  always  "  seemed  busier 
than  he  was,"  is  still  with  us.  Mediaeval  conceptions 
of  chivalry  still  govern  conduct.  The  Universal  enters 
into  the  Individual,  takes  possession  of  him,  makes  of 
him  its  temporary  manifestation. 

Nevertheless,  the  Nominalists  are  right  in  insisting 
on  the  importance  of  names.  What  we  call  the  real 
world  is  a  common  object  of  perception  and  knowledge 
to  you  and  me :  we  cannot  arrive  at  a  knowledge  of 
it  without  some  means  of  communication  with  one 
another:  our  means  of  communication  is  language. 
It  may  be  doubted  whether  even  thinking  could  go  far 
without  symbols  with  the  help  of  which  conceptions 
may  be  made  definite.  A  concept  cannot  be  explained 
without  reference  to  a  symbol.  There  is  even  a  sense 
in  which  the  Ultra-Nominalist  doctrine  that  the  indi- 
viduals in  a  class  have  nothing  in  common  but  the 
name  is  tenable.  Denotability  by  the  same  name  is  the 
only  respect  in  which  those  individuals  are  absolutely 
identical :  in  this  sense  the  name  alone  is  common  to 
them,  though  it  is  applied  in  virtue  of  their  resemblance 
to  one  another. 

Finally,  the  Conceptualists  are  right  in  insisting  on 
the  mind's  activity  in  connexion  with  general  names. 


126  Definition. 

Genera  and  species  are  not  mere  arbitrary  subjective 
collections :  the  union  is  determined  by  the  characters 
of  the  things  collected.  Still  it  is  with  the  concept  in 
each  man's  mind  that  the  name  is  connected  :  it  is  by 
the  activity  of  thought  in  recognising  likenesses  and 
forming  concepts  that  we  are  able  to  master  the 
diversity  of  our  impressions,  to  introduce  unity  into 
the  manifold  of  sense,  to  reduce  our  various  recollec- 
tions to  order  and  coherence. 

So  much  for  the  Ontological  question.  Now  for  the 
Psychological.  What  is  in  the  mind  when  we  employ 
a  general  name  ?  What  is  the  Universal  psychologi- 
cally ?  How  is  it  conceived  ? 

What  breeds  confusion  in  these  subtle  inquiries  is 
the  want  of  fixed  unambiguous  names  for  the  things  to 
be  distinguished.  It  is  only  by  means  of  such  names 
that  we  can  hold  on  to  the  distinctions,  and  keep  from 
puzzling  ourselves.  Now  there  are  three  things  to  be 
distinguished  in  this  inquiry,  which  we  may  call  the 
Concept,  the  Conception,  and  the  Conceptual  or 
Generic  Image.  Let  us  call  them  by  these  names, 
and  proceed  to  explain  them. 

By  the  Concept,  I  understand  the  meaning  of  the 
general  name,  what  the  general  name  signifies  :  by 
the  Conception,  the  mental  act  or  state  of  him  who 
conceives  this  meaning.  The  concept  of  "  triangle," 
i.e.,  what  you  and  I  mean  by  the  word,  is  not  my  act 
of  mind  or  your  act  of  mind  when  we  think  or  speak  of 
a  triangle.  The  Conception,  which  is  this  act,  is  an 
event  or  incident  in  our  mental  history,  a  psychical 
act  or  state,  a  distinct  occurrence,  a  particular  fact  in 
time  as  much  as  the  battle  of  Waterloo.  The  concept 
is  the  objective  reference  of  the  name,  which  is  the 
same,  or  at  least  is  understood  to  be  the  same,  every 


The  Controversy  about   Universals.  127 

time  we  use  it.  I  make  a  figure  on  paper  with  ink 
or  on  a  blackboard  with  chalk,  and  recognise  or  con- 
ceive it  as  a  triangle :  you  also  conceive  it  as  such  : 
we  do  the  same  to-morrow  :  we  did  the  same  yesterday  : 
each  act  of  conception  is  a  different  event,  but  the  con- 
cept is  the  same  throughout. 

Now  the  psychological  question  about  the  Universal 
is,  What  is  this  conception  ?  We  cannot  define  it 
positively  further  than  by  saying  that  it  consists  in 
realising  the  meaning  of  a  general  name :  the  act 
being  unique,  we  can  only  make  it  intelligible  by 
producing  an  example  of  it.  But  we  may  define  it 
negatively  by  distinguishing  it  from  the  conceptual 
image.  Whenever  we  conceive  anything,  "  man," 
"  horse,"  there  is  generally  present  to  our  minds  an 
image  of  a  man  or  horse,  with  accidents  of  size, 
colour,  position  or  other  categories.  But  this  concep- 
tual image  is  not  the  concept,  and  the  mental  act 
of  forming  it  is  not  conception. 

This  distinction  between  mental  picturing  or 
imaging  and  the  conception  of  common  attributes  is 
variously  expressed.  The  correlative  terms  Intuitive 
and  Symbolical  Thinking,  Presentative  and  Representative 
Knowledge  have  been  employed.1  But  whatever  terms 


1  The  only  objection  to  these  terms  is  that  they  have  slipped 
from  their  moorings  in  philosophical  usage.  Thus  instead  of 
Leibnitz's  use  of  Intuitive  and  Symbolical,  which  corresponds 
to  the  above  distinction  between  Imaging  and  Conception,  Mr. 
Jevons  employs  the  terms  to  express  a  distinction  among 
conceptions  proper.  We  can  understand  what  a  chiliagon 
means,  but  we  cannot  form  an  image  of  it  in  our  minds,  except 
in  a  very  confused  and  imperfect  way ;  whereas  we  can  form 
a  distinct  image  of  a  triangle.  Mr.  Jevons  would  call  the 
conception  of  the  triangle  Intuitive,  of  the  chiliagon  Symbolical. 


128  Definition. 

we  use,  the  distinction  itself  is  vital,  and  the  want  of 
it  leads  to  confusion. 

Thus  the  fact  that  we  cannot  form  a  conceptual 
image  composed  solely  of  common  attributes  has  been 
used  to  support  the  argument  of  Ultra-Nominalism, 
that  the  individuals  classed  under  a  common  name 
have  nothing  in  common  but  the  name.  What  the 
word  "dog"  signifies,  i.e.,  the  "concept"  of  dog,  is 
neither  big  nor  little,  neither  black  nor  tan,  neither 
here  nor  there,  neither  Newfoundland,  nor  Retriever, 
nor  Terrier,  nor  Greyhound,  nor  Pug,  nor  Bulldog. 
The  concept  consists  only  of  the  attributes  common 
to  all  dogs  apart  from  any  that  are  peculiar  to  any 
variety  or  any  individual.  Now  we  cannot  form  any 
such  conceptual  image.  Our  conceptual  image  is 
always  of  some  definite  size  and  shape.  Therefore, 
it  is  argued,  we  cannot  conceive  what  a  dog  means, 
and  dogs  have  nothing  in  common  but  the  name. 
This,  however,  does  not  follow.  The  concept  is  not 
the  conceptual  image,  and  forming  the  image  is  not 
conception.  We  may  even,  as  in  the  case  of  a 
chiliagon,  or  thousand-sided  figure,  conceive  the 
meaning  without  being  able  to  form  any  definite 
image. 

How,  then,  do  we  ordinarily  proceed  in  conceiving, 
if  we  cannot  picture  the  common  attributes  alone  and 
apart  from  particulars  ?  We  attend,  or  strive  to  attend, 
only  to  those  aspects  of  an  image  which  it  has  in 
common  with  the  individual  things  denoted.  And  if 

Again,  while  Mansel  uses  the  words  Presentative  and  Representa- 
tive to  express  our  distinction,  a  more  common  usage  is  to  call 
actual  Perception  Presentative  Knowledge,  and  ideation  or 
recollection  in  idea  Representative. 


The  Controversy  about  Universals.  129 

we  want  to  make  our  conception  definite,  we  pass  in 
review  an  indefinite  number  of  the  individuals,  case 
after  case. 

A  minor  psychological  question  concerns  the  nature 
of  the  conceptual  image.  Is  it  a  copy  of  some 
particular  impression,  or  a  confused  blur  or  blend  of 
many  ?  Possibly  neither :  possibly  it  is  something 
like  one  of  Mr.  Galton's  composite  photographs, 
photographs  produced  by  exposing  the  same  surface 
to  the  impressions  of  a  number  of  different  photographs, 
in  succession.  If  the  individuals  are  nearly  alike,  the 
result  is  an  image  that  is  not  an  exact  copy  of  any 
one  of  the  components  and  yet  is  perfectly  distinct. 
Possibly  the  image  that  comes  into  our  mind's  eye 
when  we  hear  such  a  word  as  "  horse "  or  "  man  " 
is  of  this  character,  the  result  of  the  impressions  of  a 
number  of  similar  things,  but  not  identical  with  any 
one.  As,  however,  different  persons  have  different 
conceptual  images  of  the  same  concept,  so  we  may 
have  different  conceptual  images  at  different  times. 
It  is  only  the  concept  that  remains  the  same. 

But  how,  it  may  be  asked,  can  the  concept  remain 
the  same  ?  If  the  universal  or  concept  psychologically 
is  an  intellectual  act,  repeated  every  time  we  conceive, 
what  guarantee  have  we  for  the  permanence  of  the 
concept  ?  Does  this  theory  not  do  away  with  all 
possibility  of  defining  and  fixing  concepts  ? 

This  brings  us  back  to  the  doctrine  already  laid 
down  about  the  truth  of  Realism.  The  theory  of  the 
concept  is  not  exhausted  when  it  is  viewed  only 
psychologically,  as  a  psychic  act.  If  we  would 
understand  it  fully,  we  must  consider  the  act  in  its 
relations  to  the  real  experience  of  ourselves  and 
others.  To  fix  this  act,  we  give  it  a  separate  name, 

9 


130  Definition. 

calling  it  the  conception  :  and  then  we  must  go  behind 
the  activity  of  the  mind  to  the  objects  on  which  it  is 
exercised.  The  element  of  fixity  is  found  in  them. 
And  here  also  the  truth  of  Nominalism  comes  in. 
By  means  of  words  we  enter  into  communication 
with  other  minds.  It  is  thus  that  we  discover  what 
is  real,  and  what  is  merely  personal  to  ourselves. 


PART     III. 

THE  INTERPRETATION  OF  PROPOSITIONS. 

—OPPOSITION  AND  IMMEDIATE 

INFERENCE. 


CHAPTER  I. 

THEORIES  OF  PREDICATION.— THEORIES  OF 
JUDGMENT. 

WE  may  now  return  to  the  Syllogistic  Forms,  and  the 
consideration  of  the  compatibility  or  incompatibility, 
implication,  and  interdependence  of  propositions. 

It  was  to  make  this  consideration  clear  and  simple 
that  what  we  have  called  the  Syllogistic  Form  of 
propositions  was  devised.  When  are  propositions 
incompatible  ?  When  do  they  imply  one  another  ? 
When  do  two  imply  a  third  ?  We  have  seen  in  the 
Introduction  how  such  questions  were  forced  upon 
Aristotle  by  the  disputative  habits  of  his  time.  It 
was  to  facilitate  the  answer  that  he  analysed 
propositions  into  Subject  and  Predicate,  and  viewed 
the  Predicate  as  a  reference  to  a  class  :  in  other  words, 
analysed  the 'Predicate  further  into  a  Copula  and  a 
Class  Term. 


132  The  Interpretation  of  Propositions. 

But  before  showing  how  he  exhibited  the  inter- 
connexion of  propositions  on  this  plan,  we  may  turn 
aside  to  consider  various  so-called  Theories  of  Predica- 
tion or  of  Judgment.  Strictly  speaking,  they  are  not 
altogether  relevant  to  Logic,  that  is  to  say,  as  a 
practical  science :  they  are  partly  logical,  partly 
psychological  theories  :  some  of  them  have  no  bearing 
whatever  on  practice,  but  are  matters  of  pure  scientific 
curiosity  :  but  historically  they  are  connected  with  the 
logical  treatment  of  propositions  as  having  been 
developed  out  of  this. 

The  least  confusing  way  of  presenting  these  theories 
is  to  state  them  and  examine  them  both  logically  and 
psychologically.  The  logical  question  is,  Has  the 
view  any  advantage  for  logical  purposes?  Does  it 
help  to  prevent  error,  to  clear  up  confusion  ?  Does 
it  lead  to  firmer  conceptions  of  the  truth  ?  The 
psychological  question  is,  Is  this  a  correct  theory  of 
how  men  actually  think  when  they  make  propositions  ? 
It  is  a  question  of  what  is  in  the  one  case,  and  of 
what  ought  to  be  for  a  certain  purpose  in  the  other. 

Whether  we  speak  of  Proposition  or  of  Judgment 
does  not  materially  affect  our  answer.  A  Judgment  is 
the  mental  act  accompanying  a  Proposition,  or  that 
may  be  expressed  in  a  proposition  and  cannot  be 
expressed  otherwise :  we  can  give  no  other  intelligible 
definition  or  description  of  a  judgment.  So  a  proposi- 
tion can  only  be  defined  as  the  expression  of  a  judg- 
ment :  unless  there  is  a  judgment  underneath  them,  a 
form  of  words  is  not  a  proposition. 

Let  us  take,  then,  the  different  theories  in  turn.  We 
shall  find  that  they  are  not  really  antagonistic,  but 
only  different :  that  each  is  substantially  right  from  its 
own  point  of  view  :  and  that  they  seem  to  contradict 


Theories  of  Predication.  133 

one  another  only  when  the  point  of  view  is  misunder- 
stood. 

I.  That  the  Predicate  term  may  be  regarded  as  a  class 
in   or  from  which   the   Subject  is  included  or  excluded. 
Known   as   the   Class-Inclusion,   Class-Reference,    or 
Denotative  view. 

This  way  of  analysing  propositions  is  possible,  as  we 
have  seen,  because  every  statement  implies  a  general 
name,  and  the  extension  or  denotation  of  a  general 
name  is  a  class  defined  by  the  common  attribute  or 
attributes.  It  is  useful  for  syllogistic  purposes : 
certain  relations  among  propositions  can  be  most 
simply  exhibited  in  this  way. 

But  if  this  is  called  a  Theory  of  Predication  or 
Judgment,  and  taken  psychologically  as  a  theory  of 
what  is  in  men's  minds  whenever  they  utter  a 
significant  Sentence,  it  is  manifestly  wrong.  When 
discussed  as  such,  it  is  very  properly  rejected.  When 
a  man  says  "  P  struck  Q,"  he  has  not  necessarily  a 
class  of  "  strikers  of  Q  "  definitely  in  his  mind.  What 
he  has  in  his  mind  is  the  logical  equivalent  of  this,  but 
it  is  not  this  directly.  Similarly,  Mr.  Bradley  would 
be  quite  justified  in  speaking  of  Two  Terms  and  a 
Copula  as  a  superstition,  if  it  were  meant  that  these 
analytic  elements  are  present  to  the  mind  of  an 
ordinary  speaker. 

II.  That  every  Proposition  may  be  regarded  as  affirm- 
ing or  denying  an  attribute  of  a  subject.     Known  some- 
times as  the  Connotative  or  the  Denotative-Connotative 
view.     This  also  follows  from  the  implicit  presence  of 
a  general  name  in  every  sentence.     But  it  should  not 
be  taken  as  meaning  that  the  man  who  says:  "Tom 
came  here  yesterday,"  or  "James  generally  sits  there," 
has  a  clearly  analysed   Subject  and   Attribute  in  his 


1 34  The  Interpretation  of  Propositions. 

mind.      Otherwise  it  is  as  far   wrong   as   the   other 
view. 

III.  That  every  proposition   may   be   regarded  as  an 
equation  between  two  terms.     Known  as  the  Equational 
View. 

This  is  obviously  not  true  for  common  speech  or 
ordinary  thought.  But  it  is  a  possible  way  of  regarding 
the  analytic  components  of  a  proposition,  legitimate 
enough  if  it  serves  any  purpose.  It  is  a  modification 
of  the  Class-Reference  analysis,  obtained  by  what  is 
known  as  Quantification  of  the  Predicate.  In  "All  S 
is  in  P,"  P  is  undistributed,  and  has  no  symbol  of 
Quantity.  But  since  the  proposition  imports  that 
All  S  is  a  part  of  P,  t.e.,  Some  P,  we  may,  if  we 
choose,  prefix  the  symbol  of  Quantity,  and  then  the 
proposition  may  be  read  "All  S  =  Some  P  ".  And 
so  with  the  other  forms. 

Is  there  any  advantage  in  this  ?  Yes  :  it  enables 
us  to  subject  the  formulae  to  algebraic  manipulation. 
But  any  logical  advantage — any  help  to- thinking? 
None  whatever.  The  elaborate  syllogistic  systems  of 
Boole,  De  Morgan,  and  Jevons  are  not  of  the  slightest 
use  in  helping  men  to  reason  correctly.  The  value 
ascribed  to  them  is  merely  an  illustration  of  the  Bias 
of  Happy  Exercise.  They  are  beautifully  ingenious, 
but  they  leave  every  recorded  instance  of  learned 
Scholastic  trifling  miles  behind. 

IV.  That  every  proposition   is   the  expression   of  a 
comparison    between    concepts.     Sometimes    called    the 
Conceptualist   View. 

"  To  judge,"  Hamilton  says,  "  is  to  recognise  the 
relation  of  congruence  or  confliction  in  which  two 
concepts,  two  individual  things,  or  a  concept  and  an 
individual  compared  together  stand  to  each  other." 


Theories  of  Predication.  135 

This  way  of  regarding  propositions  is  permissible  or 
not  according  to  our  interpretation  of  the  words 
"congruence"  and  "  confliction,"  and  the  word 
"  concept ".  If  by  concept  we  mean  a  conceived 
attribute  of  a  thing,  and  if  by  saying  that  two  concepts 
are  congruent  or  conflicting,  we  mean  that  they  may 
or  may  not  cohere  in  the  same  thing,  and  by  saying 
that  a  concept  is  congruent  or  conflicting  with  an 
individual  that  it  may  or  may  not  belong  to  that 
individual,  then  the  theory  is  a  corollary  from 
Aristotle's  analysis.  Seeing  that  we  must  pass 
through  that  analysis  to  reach  it,  it  is  obviously  not 
a  theory  of  ordinary  thought,  but  of  the  thought  of  a 
logician  performing  that  analysis. 

The  precise  point  of  Hamilton's  theory  was  that  the 
logician  does  not  concern  himself  with  the  question 
whether  two  concepts  are  or  are  not  as  a  matter  of 
fact  found  in  the  same  subject,  but  only  with  the 
question  whether  they  are  of  such  a  character  that 
they  may  be  found,  or  cannot  be  found,  in  the  same 
subject.  In  so  far  as  his  theory  is  sound,  it  is  an 
abstruse  and  technical  way  of  saying  that  we  may 
consider  the  consistency  of  propositions  without 
considering  whether  or  not  they  are  true,  and  that 
consistency  is  the  peculiar  business  of  syllogistic  logic. 

V.      That  the  ultimate  subject  of  every  judgment  is  reality. 

This  is  the  form  in  which  Mr.  Bradley  and  Mr. 
Bosanquet  deny  the  Ultra-Conceptualist  position. 
The  same  view  is  expressed  by  Mill  when  he  says  that 
"  propositions  are  concerned  with  things  and  not  with 
our  ideas  of  them  ". 

The  least  consideration  shows  that  there  is  justice 
in  the  view  thus  enounced.  Take  a  number  of  propo- 
sitions : — 


136  The  Interpretation  of  Propositions. 

The  streets  are  wet. 

George  has  blue  eyes. 

The  Earth  goes  round  the  Sun. 

Two  and  two  make  four. 

Obviously,  in  any  of  these  propositions,  there  is  a 
reference  beyond  the  conceptions  in  the  speaker's  mind, 
viewed  merely  as  incidents  in  his  mental  history. 
They  express  beliefs  about  things  and  the  relations 
among  things  in  rerum  natura :  when  any  one  under- 
stands them  and  gives  his  assent  to  them,  he  never 
stops  to  think  of  the  speaker's  state  of  mind,  but  of 
what  the  words  represent.  When  states  of  mind 
are  spoken  of,  as  when  we  say  that  our  ideas  are 
confused,  or  that  a  man's  conception  of  duty  influences 
his  conduct,  those  states  of  mind  are  viewed  as 
objective  facts  in  the  world  of  realities.  Even  when 
we  speak  of  things  that  have  in  a  sense  no  reality,  as 
when  we  say  that  a  centaur  is  a  combination  of  man 
and  horse,  or  that  centaurs  were  fabled  to  live  in  the 
vales  of  Thessaly,  it  is  not  the  passing  state  of  mind 
expressed  by  the  speaker  as  such  that  we  attend  to  or 
think  of;  we  pass  at  once  to  the  objective  reference  of 
the  words. 

Psychologically,  then,  the  theory  is  sound  :  what  is 
its  logical  value  ?  It  is  sometimes  put  forward  as  if  it 
were  inconsistent  with  the  Class-reference  theory  or 
the  theory  that  judgment  consists  in  a  comparison  of 
concepts.  Historically  the  origin  of  its  formal  state- 
ment is  its  supposed  opposition  to  those  theories.  But 
really  it  is  only  a  misconception  of  them  that  it  contra- 
dicts. It  is  inconsistent  with  the  Class-reference  view 
only  if  by  a  class  we  understand  an  arbitrary  subjective 
collection,  not  a  collection  of  things  on  the  ground  of 


Theories  of  Predication.  137 

common  attributes.  And  it  is  inconsistent  with  the 
Conceptualist  theory  only  if  by  a  concept  we  understand 
not  the  objective  reference  of  a  general  name,  but  what 
we  have  distinguished  as  a  conception  or  a  conceptual 
image.  The  theory  that  the  ultimate  subject  is  reality 
is  assumed  in  both  the  other  theories,  rightly  under- 
stood. If  every  proposition  is  the  utterance  of  a 
judgment,  and  every  proposition  implies  a  general 
name,  and  every  general  name  has  a  meaning  or  con- 
notation, and  every  such  meaning  is  an  attribute  of 
things  and  not  a  mental  state,  it  is  implied  that 
the  ultimate  subject  of  every  proposition  is  reality. 
But  we  may  consider  whether  or  not  proposi- 
tions are  consistent  without  considering  whether 
or  not  they  are  true,  and  it  is  only  their 
mutual  consistency  that  is  considered  in  the  syllo- 
gistic formulae.  Thus,  while  it  is  perfectly  correct 
to  say  that  every  proposition  expresses  either  truth  or 
falsehood,  or  that  the  characteristic  quality  of  a  judg- 
ment is  to  be  true  or  false,  it  is  none  the  less  correct  to 
say  that  we  may  temporarily  suspend  consideration  of 
truth  or  falsehood,  and  that  this  is  done  in  what  is 
commonly  known  as  Formal  Logic. 

VI.  That  every  proposition  may  be  regarded  as 
expressing  relations  between  phenomena. 

Bain  follows  Mill  in  treating  this  as  the  final 
import  of  Predication.  But  he  indicates  more 
accurately  the  logical  value  of  this  view  in  speaking 
of  it  as  important  for  laying  out  the  divisions  of 
Inductive  Logic.  They  differ  slightly  in  their  lists 
of  Universal  Predicates  based  upon  Import  in  this 
sense — Mill's  being  Resemblance,  Coexistence,  Simple 
Sequence,  and  Causal  Sequence,  and  Bain's  being 
Coexistence,  Succession,  and  Equality  or  Inequality. 


138  The  Interpretation  of  Propositions. 

But  both  lay  stress,  upon  Coexistence  and  Succession, 
and  we  shall  find  that  the  distinctions  between  Simple 
Sequence  and  Causal  Sequence,  and  between  Repeated 
and  Occasional  Coexistence,  are  all-important  in  the 
Logic  of  Investigation.  But  for  syllogistic  purposes- 
the  distinctions  have  no  relevance. 


CHAPTER  II. 

THE  "  OPPOSITION  "  OF  PROPOSITIONS.— THE 
INTERPRETATION    OF   "NO". 

PROPOSITIONS  are  technically  said  to  be  "  opposed " 
when,  having  the  same  terms  in  Subject  and  Predicate, 
they  differ  in  Quantity,  or  in  Quality,  or  in  both.1 

1  This  is  the  traditional  definition  of  Opposition  from  an  early 
period,  though  the  tradition  does  not  start  from  Aristotle.  With 
him  opposition  (avriKeiffQat)  meant,  as  it  still  means  in  ordinary 
speech,  incompatibility.  The  technical  meaning  of  Opposition  is 
based  on  the  diagram  (given  afterwards  in  the  text)  known  as  the 
Square  of  Opposition,  and  probably  originated  in  a  confused 
apprehension  of  the  reason  why  it  received  that  name.  It  was 
called  the  Square  of  Opposition,  because  it  was  intended  to 
illustrate  the  doctrine  of  Opposition  in  Aristotle's  sense  and  the 
ordinary  sense  of  repugnance  or  incompatibility.  What  the 
Square  brings  out  is  this.  If  the  four  forms  A  E  I  O  are  arranged 
symmetrically  according  as  they  differ  in  quantity,  or  quality, 
or  both,  it  is  seen  that  these  differences  do  not  correspond 
symmetrically  to  compatibility  and  incompatibility:  that  pro- 
positions may  differ  in  quantity  or  in  quality  without  being 
incompatible,  and  that  they  may  differ  in  both  (as  Contradictories) 
and  be  less  violently  incompatible  than  when  they  differ  in  one 
only  (as  Contraries).  The  original  purpose  of  the  diagram  was 
to  bring  this  out,  as  is  done  in  every  exposition  of  it.  Hence  it 
was  called  the  Square  of  Opposition.  But  as  a  descriptive  title 
this  is  a  misnomer  :  it  should  have  been  the  Square  of  Differences 
in  Quantity  or  Quality.  This  misnomer  has  been  perpetuated  by 
appropriating  Opposition  as  a  common  name  for  difference  in 
Quantity  or  Quality  when  the  terms  are  the  same  and  in  the  same 
(139) 


140  The  Interpretation  of  Propositions. 

The  practical  question  from  which  the  technical 
doctrine  has  been  developed  was  how  to  determine 
the  significance  of  contradiction.  What  is  meant  by 
giving  the  answer  "  No  "  to  a  proposition  put  interro- 
gatively ?  What  is  the  interpretation  of  "No"? 
What  is  the  respondent  committed  to  thereby  ? 

"  Have  all  ratepayers  a  vote  ? "  If  you  answer 
"  No,"  you  are  bound  to  admit  that  some  ratepayers 
have  not.  O  is  the  Contradictory  of  A.  If  A  is  false, 

0  must  be  true.     So  if  you  deny  O,  you  are  bound  to 
admit  A :  one  or  other  must  be  true  :  either  Some  rate- 
payers have  not  a  vote  or  All  have. 

Is  it  the  case  that  no  man  can  live  without  sleep  ? 
Deny  this,  and  you  commit  yourself  to  maintaining 
that  Some  man,  one  at  least,  can  live  without  sleep. 

1  is  the  Contradictory  of  E  ;  and  vice  versa. 

Contradictory  opposition  is  distinguished  from  Con- 
trary, the  opposition  of  one  Universal  to  another,  of 
A  to  E  and  E  to  A.  There  is  a  natural  tendency  to 
meet  a  strong  assertion  with  the  very  reverse.  Let  it 
be  maintained  that  women  are  essentially  faithless  or 
that  "  the  poor  in  a  lump  is  bad,"  and  disputants  are 
apt  to  meet  this  extreme  with  another,  that  constancy 
is  to  be  found  only  in  women  or  true  virtue  only  among 
the  poor.  Both  extremes,  both  A  and  E,  may  be  false  : 
the  truth  may  lie  between  :  Some  are,  Some  not. 

order,  and  distinguishing  it  in  this  sense  from  Repugnance  or 
Incompatibility  (Tataretusin  Summulas,  DeOppositionibus  {150-1], 
Keynes,  The  Opposition  of  Propositions  [1887]).  Seeing  that  there 
never  is  occasion  to  speak  of  Opposition  in  the  limited  sense 
except  in  connexion  with  the  Square,  there  is  no  real  risk  ot 
confusion.  A  common  name  is  certainly  wanted  in  that  connexion, 
if  only  to  say  that  Opposition  (in  the  limited  or  diagrammatic 
sense)  does  not  mean  incompatibility. 


The  "Opposition"  of  Propositions.  141 

Logically,  the  denial  of  A  or  E  implies  only  the 
admission  of  O  or  I.  You  are  not  committed  to  the 
full  contrary.  But  the  implication  of  the  Contradictory 
is  absolute ;  there  is  no  half-way  house  where  the 
truth  may  reside.  Hence  the  name  of  Excluded 
Middle  is  applied  to  the  principle  that  "Of  two  Con- 
tradictories one  or  other  must  be  true :  they  cannot 
both  be  false  ". 

While  both  Contraries  may  be  false,  they  cannot 
both  be  true. 

It  is  sometimes  said  that  in  the  case  of  Singular 
propositions,  the  Contradictory  and  the  Contrary 
coincide.  A  more  correct  doctrine  is  that  in  the  case 
of  Singular  propositions,  the  distinction  is  not  needed 
and  does  not  apply.  Put  the  question  "  Is  Socrates 
wise?"  or  "Is  this  paper  white?"  and  the  answer 
"  No"  admits  of  only  one  interpretation,  provided  the 
terms  remain  the  same.  Socrates  may  become  foolish, 
or  this  paper  may  hereafter  be  coloured  differently,  but 
in  either  case  the  subject  term  is  not  the  same  about 
which  the  question  was  asked.  Contrary  opposition 
belongs  only  to  general  terms  taken  universally  as 
subjects.  Concerning  individual  subjects  an  attribute 
must  be  either  affirmed  or  denied  simply  :  there  is  no 
middle  course.  Such  a  proposition  as  "  Socrates  is 
sometimes  not  wise,"  is  not  a  true  Singular  proposition, 
though  it  has  a  Singular  term  as  grammatical  subject. 
Logically,  it  is  a  Particular  proposition,  of  which  the 
subject-term  is  the  actions  or  judgments  of  Socrates.1 

1Cp.  Keynes,  pt.  ii.  ch.  ii.  s.  57.  Aristotle  laid  down  the  dis- 
tinction between  Contrary  and  Contradictory  to  meet  another 
quibble  in  contradiction,  based  on  taking  the  Universal  as  a  whole 
and  indivisible  subject  like  an  Individual,  of  which  a  given  predi- 
cate must  be  either  affirmed  or  denied. 


142 


The  Interpretation  of  Propositions. 


Opposition,  in  the  ordinary  sense,  is  the  opposition  of 
incompatible  propositions,  and  it  was  with  this  only 
that  Aristotle  concerned  himself.  But  from  an  early 
period  in  the  history  of  Logic,  the  word  was  extended 
to  cover  mere  differences  in  Quantity  and  Quality 
among  the  four  forms  A  E  I  O,  which  differences  have 
been  named  and  exhibited  symmetrically  in  a  diagram 
known  as  :  The  Square  of  Opposition. 


A...  ...Contraries 


I 

CO 


V) 


I Sub-contraries 6 

The  four  forms  being  placed  at  the  four  corners  of 
the  Square,  and  the  sides  and  diagonals  representing 
relations  between  them  thus  separated,  a  very  pretty 
and  symmetrical  doctrine  is  the  result. 

Contradictories,  A  and  O,  E  and  I,  differ  both  in 
Quantity  and  in  Quality. 

Contraries,  A  and  E,  differ  in  Quality  but  not  in 
Quantity,  and  are  both  Universal. 

Sub-contraries,  I  and  O,  differ  in  Quality  but  not  in 
Quantity,  and  are  both  Particular. 


The  "  Opposition  "  of  Propositions.  143 

Subalterns,  A  and  I,  E  and  O,  differ  in  Quantity  but 
not  in  Quality. 

Again,  in  respect  of  concurrent  truth  and  falsehood 
there  is  a  certain  symmetry. 

Contradictories  cannot  both  be  true,  nor  can  they 
both  be  false. 

Contraries  may  both  be  false,  but  cannot  both  be  true. 

Sub-contraries  may  both  be  true,  but  cannot  both  be 
false. 

Subalterns  may  both  be  false  and  both  true.  If  the 
Universal  is  true,  its  subalternate  Particular  is  true : 
but  the  truth  of  the  Particular  does  not  similarly  imply 
the  truth  of  its  Subalternating  Universal. 

This  last  is  another  way  of  saying  that  the  truth  of 
the  Contrary  involves  the  truth  of  the  Contradictory, 
but  the  truth  of  the  Contradictory  does  not  imply  the 
truth  of  the  Contrary. 

There,  however,  the  symmetry  ends.  The  sides 
and  the  diagonals  of  the  Square  do  not  symmetrically 
represent  degrees  of  incompatibility,  or  opposition  in 
the  ordinary  sense. 

There  is  no  incompatibility  between  two  Sub- 
contraries  or  a  Subaltern  and  its  Subalternant.  Both 
may  be  true  at  the  same  time.  Indeed,  as  Aristotle 
remarked  of  I  and  O,  the  truth  of  the  one  commonly 
implies  the  truth  of  the  other :  to  say  that  some  of  the 
crew  were  drowned,  implies  that  some  were  not,  and 
wee  versa.  Subaltern  and  Subalternant  also  are  com- 
patible, and  something  more.  If  a  man  has  admitted 
A  or  E,  he  cannot  refuse  to  admit  I  or  O,  the  Particular 
of  the  same  Quality.  If  All  poets  are  irritable,  it 
cannot  be  denied  that  some  are  so ;  if  None  is,  that 
Some  are  not.  The  admission  of  the  Contrary  includes 
the  admission  of  the  Contradictory. 


144  The  Interpretation  of  Propositions. 

Consideration  of  Subalterns,  however,  brings  to 
light  a  nice  ambiguity  in  Some.  It  is  only  when  I  is 
regarded  as  the  Contradictory  of  E,  that  it  can  properly 
be  said  to  be  Subalternate  to  A.  In  that  case  the 
meaning  of  Some  is  "  not  none,"  i.e.,  "  Some  at  least ". 
But  when  Some  is  taken  as  the  sign  of  Particular 
quantity  simply,  i.e.,  as  meaning  "  not  all,"  or  "  some 
at  most,"  I  is  not  Subalternate  to  A,  but  opposed  to  it 
in  the  sense  that  the  truth  of  the  one  is  incompatible 
with  the  truth  of  the  other. 

Again,  in  the  diagram  Contrary  opposition  is  repre- 
sented by  a  side  and  Contradictory  by  the  diagonal ; 
that  is  to  say,  the  stronger  form  of  opposition  by  the 
shorter  line.  The  Contrary  is  more  than  a  denial : 
it  is  a  counter-assertion  of  the  very  reverse,  TO  evavnov. 
"  Are  good  administrators  always  good  speakers  ?  " 
"  On  the  contrary,  they  never  are."  This  is  a  much 
stronger  opposition,  in  the  ordinary  sense,  than  a 
modest  contradictory,  which  is  warranted  by  the 
existence  of  a  single  exception.  If  the  diagram  were 
to  represent  incompatibility  accurately,  the  Contrary 
ought  to  have  a  longer  line  than  the  Contradictory, 
and  this  it  seems  to  have  had  in  the  diagram  that 
Aristotle  had  in  mind  (JDe  Interpret.,  c.  10). 

It  is  only  when  Opposition  is  taken  to  mean  merely 
difference  in  Quantity  and  Quality  that  there  can  be 
said  to  be  greater  opposition  between  Contradictories 
than  between  Contraries.  Contradictories  differ  both 
in  Quantity  and  in  Quality  :  Contraries,  in  Quality 
only. 

There  is  another  sense  in  which  the  Particular 
Contradictory  may  be  said  to  be  a  stronger  opposite 
than  the  Contrary.  It  is  a  stronger  position  to  take 
up  argumentatively.  It  is  easier  to  defend  than  a 


The  "  Opposition  "  of  Propositions.  145 

Contrary.      But  this  is  because  it  offers  a  narrower 
and  more  limited  opposition. 

We  deal  with  what  is  called  Immediate  Inference 
in  the  next  chapter.  Pending  an  exact  definition  of 
the  process,  it  is  obvious  that  two  immediate  inferences 
are  open  under  the  above  doctrines,  (i)  Granted  the 
truth  of  any  proposition,  you  may  immediately  infer 
the  falsehood  of  its  Contradictory.  (2)  Granted  the 
truth  of  any  Contrary,  you  may  immediately  infer  the 
truth  of  its  Subaltern.1 


1 1  have  said  that  there  is  little  risk  of  confusion  in  using  the 
word  Opposition  in  its  technical  or  limited  sense.  There  is, 
however,  a  little.  When  it  is  said  that  these  inferences  are  based 
on  Opposition,  or  that  Opposition  is  a  mode  of  Immediate  Infer- 
ence, there  is  confusion  of  ideas  unless  it  is  pointed  out  that  when 
this  is  said,  it  is  Opposition  in  the  ordinary  sense  that  is  meant. 
The  inferences  are  really  based  on  the  rules  of  Contrary  and 
Contradictory  Opposition  ;  Contraries  cannot  both  be  true,  and 
of  Contradictories  one  or  other  must  be. 


10 


CHAPTER  III. 

THE  IMPLICATION  OF   PROPOSITIONS.— IMMEDIATE 
FORMAL  INFERENCE.— EDUCTION. 

THE  meaning  of  Inference  generally  is  a  subject  of 
dispute,  and  to  avoid  entering  upon  debatable  ground 
at  this  stage,  instead  of  attempting  to  define  Inference 
generally,  I  will  confine  myself  to  defining  what  is 
called  Formal  Inference,  about  which  there  is  com- 
paratively little  difference  of  opinion. 

Formal  Inference  then  is  the  apprehension  of  what 
is  implied  in  a  certain  datum  or  admission  :  the 
derivation  of  one  proposition,  called  the  Conclusion, 
from  one  or  more  given,  admitted,  or  assumed  pro- 
positions, called  the  Premiss  or  Premisses. 

When  the  conclusion  is  drawn  from  one  proposition, 
the  inference  is  said  to  be  immediate  ;  when  more  than 
one  proposition  is  necessary  to  the  conclusion,  the 
inference  is  said  to  be  mediate. 

Given  the  proposition,  "All  poets  are  irritable,"  we 
can  immediately  infer  that  "  Nobody  that  is  not 
irritable  is  a  poet "  ;  and  the  one  admission  implies 
the  other.  But  we  cannot  infer  immediately  that 
"  all  poets  make  bad  husbands  ".  Before  we  can  do 
this  we  must  have  a  second  proposition  conceded, 


The  Implication  of  Propositions.  147 

that  "All  irritable  persons  make  bad  husbands". 
The  inference  in  the  second  case  is  called  Mediate.1 

The  modes  and  conditions  of  valid  Mediate  Infer- 
ence constitute  Syllogism,  which  is  in  effect  the 
reasoning  together  of  separate  admissions.  With  this 
we  shall  deal  presently.  Meantime  of  Immediate 
Inference. 

To  state  all  the  implications  of  a  certain  form  of 
proposition,  to  make  explicit  all  that  it  implies,  is  the 
same  thing  with  showing  what  immediate  inferences 
from  it  are  legitimate.  Formal  inference,  in  short,  is 
the  eduction  of  all  that  a  proposition  implies. 

Most  of  the  modes  of  Immediate  Inference  formu- 
lated by  logicians  are  preliminary  to  the  Syllogistic 
process,  and  have  no  other  practical  application.  The 
most  important  of  them  technically  is  the  process 
known  as  Conversion,  but  others  have  been  judged 
worthy  of  attention. 

^EQUIPOLLENT  OR  EQUIVALENT    FORMS — OBVERSION. 

^Equipollence  or  Equivalence  (I<roSwa/u'a)  is  defined 
as  the  perfect  agreement  in  sense  of  two  propositions 
that  differ  somehow  in  expression.2 

The  history  of  ^Equipollence  in  logical  treatises 
illustrates  two  tendencies.  There  is  a  tendency  on 
the  one  hand  to  narrow  a  theme  down  to  definite  and 
manageable  forms.  But  when  a  useful  exercise  is 
discarded  from  one  place  it  has  a  tendency  to  break 
out  in  another  under  another  name.  A  third  tendency 

1  I  purposely  chose  disputable  propositions  to  emphasise  the 
fact  that  Formal  Logic  has  no  concern  with  the  truth,  but  only 
with  the  interdependence  of  its  propositions. 

2  Mark  Duncan,  Inst.  Log.,  ii.  5,  1612. 


148  The  Interpretation  of  Propositions. 

may  also  be  said  to  be  specially  well  illustrated — the 
tendency  to  change  the  traditional  application  of  logical 
terms. 

In  accordance  with  the  above  definition  of  ^Equi- 
pollence  or  Equivalence,  which  corresponds  with 
ordinary  acceptation,  the  term  would  apply  to  all  cases 
of  "  identical  meaning  under  difference  of  expression  ". 
Most  examples  of  the  reduction  of  ordinary  speech 
into  syllogistic  form  would  be  examples  of  aequipol- 
lence ;  all,  in  fact,  would  be  so  were  it  not  that  ordinary 
speech  loses  somewhat  in  the  process,  owing  to  the 
indefiniteness  of  the  syllogistic  symbol  for  particular 
quality,  Some.  And  in  truth  all  such  transmutations 
of  expression  are  as  much  entitled  to  the  dignity  of 
being  called  Immediate  Inferences  as  most  of  the 
processes  so  entitled. 

Dr.  Bain  uses  the  word  with  an  approach  to  this 
width  of  application  in  discussing  all  that  is  now  most 
commonly  called  Immediate  Inference  under  the  title 
of  Equivalent  Forms.  The  chief  objection  to  this 
usage  is  that  the  Converse  per  accidens  is  not  strictly 
equivalent.  A  debater  may  want  for  his  argument  less 
than  the  strict  equivalent,  and  content  himself  with 
educing  this  much  from  his  opponent's  admission. 
(Whether  Dr.  Bain  is  right  in  treating  the  Minor  and 
Conclusion  of  a  Hypothetical  Syllogism  as  being 
equivalent  to  the  Major,  is  not  so  much  a  question  of 
naming.) 

But  in  the  history  of  the  subject,  the  traditional 
usage  has  been  to  confine  ^quipollence  to  cases  of 
equivalence  between  positive  and  negative  forms  of 
expression.  "  Not  all  are,"  is  equivalent  to  "  Some 
are  not "  :  "  Not  none  is,"  to  "  Some  are  ".  In  Pre- 
Aldrichian  text-books,  ^Equipollence  corresponds 


The  Implication  of  Propositions.  149 

mainly  to  what  it  is  now  customary  to  call  (e.g., 
Fowler,  pt.  iii.  c.  ii.,  Keynes,  pt.  ii.  c.  vii.)  Immediate 
Inference  based  on  Opposition.  The  denial  of  any 
proposition  involves  the  admission  of  its  contradictory. 
Thus,  if  the  negative  particle  "  Not"  is  placed  before 
the  sign  of  Quantity,  All  or  Some,  in  a  proposition, 
the  resulting  proposition  is  equivalent  to  the  Contra- 
dictory of  the  original.  Not  all  S  is  P  =  Some  S  is 
not  P.  Not  any  S  is  P  =  No  S  is  P.  The  mediaeval 
logicians  tabulated  these  equivalents,  and  also  the 
forms  resulting  from  placing  the  negative  particle 
after,  or  both  before  and  after,  the  sign  of  Quantity. 
Under  the  title  of  ^quipollence,  in  fact,  they  con- 
sidered the  interpretation  of  the  negative  particle 
generally.  If  the  negative  is  placed  after  the  universal 
sign,  it  results  in  the  Contrary :  if  both  before  and 
after,  in  the  Subaltern.  The  statement  of  these 
equivalents  is  a  puzzling  exercise  which  no  doubt 
accounts  for  the  prominence  given  it  by  Aristotle  and 
the  Schoolmen.  The  latter  helped  the  student  with 
the  following  Mnemonic  line :  Free  Contradic.,  post 
Contrar.,  pr<z  postque  Subaltern^ 

1  There  can  be  no  doubt  that  in  their  doctrine  of  ^quipollents, 
the  Schoolmen  were  trying  to  make  plain  a  real  difficulty  in  inter- 
pretation, the  interpretation  of  the  force  of  negatives.  Their  results 
would  have  been  more  obviously  useful  if  they  had  seen  their  way 
to  generalising  them.  Perhaps  too  they  wasted  their  strength  in 
applying  it  to  the  artificial  syllogistic  forms,  which  men  do  not 
ordinarily  encounter  except  in  the  manipulation  of  syllogisms. 
Their  results  might  have  been  generalised  as  follows  : — 

(1)  A  "not"  placed  before  the  sign  of  Quantity  contradicts  the 
whole  proposition.     Not  "All  S  is  P,"  not  "No  S  is  P,"  not 
"  Some  S  is  P,"  not  "  Some  S  is  not  P,"  are  equivalent  respec- 
tively to  contradictories  of  the  propositions  thus  negatived. 

(2)  A   "  not "    placed   after   the   sign  of  Quantity  affects   the 


150  The  Interpretation  of  Propositions. 

To  ^Equipollence  belonged  also  the  manipulation 
of  the  forms  known  after  the  Summula  as  Exponibiles ', 
notably  Exclusive  and  Exceptive  propositions,  such  as 
None  but  barristers  are  eligible,  The  virtuous  alone 
are  happy.  The  introduction  of  a  negative  particle 
into  these  already  negative  forms  makes  a  very  trying 
problem  in  interpretation.  The  aequipollence  of  the 
Exponibiles  was  dropped  from  text-books  long  before 
Aldrich,  and  it  is  the  custom  to  laugh  at  them  as 
extreme  examples  of  frivolous  scholastic  subtlety  :  but 
most  modern  text-books  deal  with  part  of  the  doctrine 
of  the  Exponibiles  in  casual  exercises. 

Curiously  enough,  a  form  left  unnamed  by  the 
scholastic  logicians  because  too  simple  and  useless, 
has  the  name  ./Equipollent  appropriated  to  it,  and  to 
it  alone,  by  Ueberweg,  and  has  been  adopted  under 
various  names  into  all  recent  treatises. 

Bain  calls  it  the  Formal  Obverse,1  and  the  title  of 


copula,  and  amounts  to  inverting  its  Quality,  thus  denying  the 
predicate  term  of  the  same  quantity  of  the  subject  term  of  which 
it  was  originally  affirmed,  and  vice  versa. 

All  S  is  "  not "  P  =  No  S  is  P. 
No  S  is  "  not "  P  =  All  S  is  P. 
Some  S  is  "  not "  P  =  Some  S  is  not  P. 
Some  S  is  "  not "  not  P  =  Some  S  is  P. 

(3)  If  a  "  not "  is  placed  before  as  well  as  after,  the  resulting 
forms  are  obviously  equivalent  (under  Rule  i)  to  the  assertion  of 
the  contradictories  of  the  forms  on  the  right  (in  the  illustration  of 
Rule  2). 


Not 
Not 
Not 
Not 


All  S  is  "  not "  P          =  No  S  is  P 
No  S  is"  not  "P          =  All  S  is  P 
Some  S  is  "  not"  P     =  Some  Sis  not  P 
Some  S  is  "  not "  not  P  =  Some  S  is  P 


=  Some  S  is  P. 
=  Some  Sis  not  P. 
=  All  S  is  P. 
=  No  S  is  P. 


1  Formal  to  distinguish  it   from  what  he  called  the  Material 
Obverse,  about  which   more  presently. 


The  Implication  of  Propositions.  151 

ObYersion  (which  has  the  advantage  of  rhyming  with 
Conversion)  has  been  adopted  by  Keynes,  Miss 
Johnson,  and  others. 

Fowler  (following  Karslake)  calls  it  Permutation. 
The  title  is  not  a  happy  one,  having  neither  rhyme 
nor  reason  in  its  favour,  but  it  is  also  extensively  used. 

This  immediate  inference  is  a  very  simple  affair  to 
have  been  honoured  with  such  a  choice  of  terminology. 
"  This  road  is  long :  therefore,  it  is  not  short,"  is  an 
easy  inference  :  the  second  proposition  is  the  Obverse, 
or  Permutation,  or  ^Equipollent,  or  (in  Jevons's  title) 
the  Immediate  Inference  by  Privative  Conception,  of 
the  first. 

The  inference,  such  as  it  is,  depends  on  the  Law  of 
Excluded  Middle.  Either  a  term  P,  or  its  contradic- 
tory, not-P,  must  be  true  of  any  given  subject,  S  : 
hence  to  affirm  P  of  all  or  some  S,  is  equivalent  to 
denying  not-P  of  the  same  :  and,  similarly,  to  deny  P, 
is  to  affirm  not-P.  Hence  the  rule  of  Obversion  ; 
—Substitute  for  the  predicate  term  its  Contrapositive,  * 
and  change  the  Quality  of  the  proposition. 

All  S  is  P  =  No  S  is  not-P. 
No  S  is  P  =  All  S  is  not-P. 
Some  S  is  P  =  Some  S  is  not  not-P. 
Some  S  is  not  P  =  Some  S  is  not-P. 

CONVERSION. 

The  process  takes  its  name  from  the  interchange  of 
the  terms.  The  Predicate-term  becomes  the  Subject- 
term,  and  the  Subject-term  the  Predicate-term. 

When   propositions  are  analysed  into    relations  of 

1  The  mediaeval  word  for  the  opposite  of  a  term,  the  word 
Contradictory  being  confined  to  the  prepositional  form. 


152  The  Interpretation  of  Propositions. 

inclusion  or  exclusion  between  terms,  the  assertion 
of  any  such  relation  between  one  term  and  another, 
implies  a  Converse  relation  between  the  second  term 
and  the  first.  The  statement  of  this  implied  assertion 
is  technically  known  as  the  Converse  of  the  original 
proposition,  which  may  be  called  the  Convertend. 

Three  modes  of  Conversion  are  commonly  recog- 
nised : — (a)  Simple  Conversion ;  (b)  Conversion  per 
acridens  or  by  limitation  ;  (c]  Conversion  by  Contra- 
position. 

(a)  E  and  I  can  be  simply  converted,  only  the  terms 
being  interchanged,  and  Quantity  and  Quality  remain- 
ing the  same. 

If  S  is  wholly  excluded  from  P,  P  must  be  wholly 
excluded  from  S.  If  Some  S  is  contained  in  P,  then 
Some  P  must  be  contained  in  S. 

(b)  A  cannot  be  simply  converted.     To  know  that 
All   S   is  contained  in   P,   gives  you  no  information 
about  that  portion  of  P  which  is  outside  S.     It  only 
enables  you  to  assert  that  Some  P  is  S  ;  that  portion 
of  P,  namely,  which  coincides  with  S. 

O  cannot  be  converted  either  simply  or  per  accidens. 
Some  S  is  not  P  does  not  enable  you  to  make  any 
converse  assertion  about  P.  All  P  may  be  S,  or  No 
P  may  be  S,  or  Some  P  may  be  not  S.  All  the  three 
following  diagrams  are  compatible  with  Some  S  being 
excluded  from  P. 


(c)  Another  mode  of  Conversion,  known  by  mediaeval 
logicians  following   Boethius  as   Conversio  per  contra- 


The  Implication  of  Propositions.  153 

positionem  terminorum,  is  useful  in  some  syllogistic 
manipulations.  This  Converse  is  obtained  by  substi- 
tuting for  the  predicate  term  its  Contrapositive  or 
Contradictory,  not-P,  making  the  consequent  change 
of  Quality,  and  simply  converting.  Thus  All  S  is  P 
is  converted  into  the  equivalent  No  not-P  is  S.1 

Some  have  called  it  "  Conversion  by  Negation,"  but 
"  negation "  is  manifestly  too  wide  and  common  a 
word  to  be  thus  arbitrarily  restricted  to  the  process  of 
substituting  for  one  term  its  opposite. 

Others  (and  this  has  some  mediaeval  usage  in  its 
favour,  though  not  the  most  intelligent)  would  call 
the  form  All  not-P  is  not-S  (the  Obverse  or  Permu- 
tation of  No  not-P  is  S),  the  Converse  by  Contra- 
position. This  is  to  conform  to  an  imaginary  rule 
that  in  Conversion  the  Converse  must  be  of  the  same 
Quality  with  the  Convertend.  But  the  essence  of 
Conversion  is  the  interchange  of  Subject  and  Predicate  : 
the  Quality  is  not  in  the  definition  except  by  a  bungle : 
it  is  an  accident.  No  not-P  is  S,  and  Some  not-P  is 
S  are  the  forms  used  in  Syllogism,  and  therefore 
specially  named.  Unless  a  form  had  a  use,  it 
was  left  unnamed,  like  the  Subalternate  forms  of 
Syllogism :  Nomen  habent  nullum :  nee,  si  bene 
colligis,  usum. 


1  It  is  to  be  regretted  that  a  practice  has  recently  crept  in  of 
calling  this  form,  for  shortness,  the  Contrapositive  simply.  By 
long-established  usage,  dating  from  Boethius,  the  word  Contra- 
positive  is  a  technical  name  for  a  terminal  form,  not-A,  and  it  is 
still  wanted  for  this  use.  There  is  no  reason  why  the  preposi- 
tional form  should  not  be  called  the  Converse  by  Contraposition, 
or  the  Contrapositive  Converse,  in  accordance  with  traditional 
usaee. 


154  The  Interpretation  of  Propositions. 

TABLE  OF  CONTRAPOSITIVE  CONVERSES. 

Con.  Con. 

All  S  is  P  No  not-P  is  S 

No  S  is  P  Some  not-P  is  S 

Some  S  is  not  P  Some  not-P  is  S 

Some  S  is  P  None. 

When  not-P  is  substituted  for  P,  Some  S  is  P 
becomes  Some  S  is  not  not-P,  and  this  form  is 
inconvertible. 

OTHER  FORMS  OF  IMMEDIATE  INFERENCE. 

I  have  already  spoken  of  the  Immediate  Inferences 
based  on  the  rules  of  Contradictory  and  Contrary 
Opposition  (see  p.  145). 

Another  process  was  observed  by  Thomson,  and 
named  Immediate  Inference  by  Added  Determinants. 
If  it  is  granted  that  "A  negro  is  a  fellow-creature," 
it  follows  that  "  A  negro  in  suffering  is  a  fellow- 
creature  in  suffering  ".  But  that  this  does  not  follow 
for  every  attribute1  is  manifest  if  you  take  another 
case  : — "  A  tortoise  is  an  animal :  therefore,  a  fast 
tortoise  is  a  fast  animal "  The  form,  indeed,  holds 
in  cases  not  worth  specifying  :  and  is  a  mere  handle 
for  quibbling.  It  could  not  be  erected  into  a  general 
rule  unless  it  were  true  that  whatever  distinguishes  a 
species  within  a  class,  will  equally  distinguish  it  in 
every  class  in  which  the  first  is  included. 

Modal  Consequence  has  also  been  named  among 
the  forms  of  Immediate  Inference.  By  this  is  meant 
the  inference  of  the  lower  degrees  of  certainty  from  the 

1  Cf.  Stock,  part  iii.  c.  vii. ;   Bain,  Deduction,  p.  109. 


The  Implication  of  Propositions.  155 

higher.     Thus   must  be  is  said  to  imply  may  be;  and 
None  can  be  to  imply  None  is. 

Dr.  Bain  includes  also  Material  Obversion^  the 
analogue  of  Formal  Obversion  applied  to  a  Subject. 
Thus  Peace  is  beneficial  to  commerce,  implies  that 
War  is  injurious  to  commerce.  Dr.  Bain  calls  this 
Material  Obversion  because  it  cannot  be  practised 
safely  without  reference  to  the  matter  of  the  proposition. 
We  shall  recur  to  the  subject  in  another  chapter. 


CHAPTER  IV. 
THE  COUNTER-IMPLICATION  OF  PROPOSITIONS. 

IN  discussing  the  Axioms  of  Dialectic,  I  indicated  that 
the  propositions  of  common  speech  have  a  certain 
negative  implication,  though  this  does  not  depend 
upon  any  of  the  so-called  Laws  of  Thought,  Identity, 
Contradiction,  and  Excluded  Middle.  Since,  however, 
the  counter-implicate  is  an  important  guide  in  the 
interpretation  of  propositions,  it  is  desirable  to  recog- 
nise it  among  the  modes  of  Immediate  Inference. 

I  propose,  then,  first,  to  show  that  people  do 
ordinarily  infer  at  once  to  a  counter-sense  ;  second,  to 
explain  briefly  the  Law  of  Thought  on  which  such  an 
inference  is  justified  ;  and,  third,  how  this  law  may  be 
applied  in  the  interpretation  of  propositions,  with  a 
view  to  making  subject  and  predicate  more  definite. 

Every  affirmation  about  anything  is  an  implicit 
negation  about  something  else.  Every  say  is  a  gain- 
say. That  people  ordinarily  act  upon  this  as  a  rule  o 
interpretation  a  little  observation  is  sufficient  to  show : 
and  we  find  also  that  those  who  object  to  having  their 
utterances  interpreted  by  this  rule  often  shelter  them- 
selves under  the  name  of  Logic. 

Suppose,  for  example,  that  a  friend  remarks,  when 
the  conversation  turns  on  children,  that  John  is  a  good 
boy,  the  natural  inference  is  that  the  speaker  has  in  his 


The  Counter- Implication  of  Propositions.          157 

mind  another  child  who  is  not  a  good  boy.  Such  an 
inference  would  at  once  be  drawn  by  any  actual  hearer, 
and  the  speaker  would  protest  in  vain  that  he  said 
nothing  about  anybody  but  John.  Suppose  there  are 
two  candidates  for  a  school  appointment,  A  and  B, 
and  that  stress  is  laid  upon  the  fact  that  A  is  an 
excellent  teacher.  A's  advocate  would  at  once  be 
understood  to  mean  that  B  was  not  equally  excellent 
as  a  teacher. 

The  fairness  of  such  inferences  is  generally  recog- 
nised. A  reviewer,  for  example,  of  one  of  Mrs. 
Oliphant's  historical  works,  after  pointing  out  some 
small  errors,  went  on  to  say  that  to  confine  himself  to 
censure  of  small  points,  was  to  acknowledge  by  impli- 
cation that  there  were  no  important  points  to  find 
fault  with. 

Yet  such  negative  implications  are  often  repudiated 
as  illogical.  It  would  be  more  accurate  to  call  them 
extra-logical.  They  are  not  condemned  by  any  logical 
doctrine  :  they  are  simply  ignored.  They  are  extra- 
logical  only  because  they  are  not  legitimated  by  the 
Laws  of  Identity,  Contradiction,  and  Excluded  Middle: 
and  the  reason  why  Logic  confines  itself  to- those  laws 
is  that  they  are  sufficient  for  Syllogism  and  its  subsidiary 
processes. 

But,  though  extra-logical,  to  infer  a  counter-implicate 
is  not  unreasonable  :  indeed,  if  Definition,  clear  vision 
of  things  in  their  exact  relations,  is  our  goal  rather 
than  Syllogism,  a  knowledge  of  the  counter-implicate 
is  of  the  utmost  consequence.  Such  an  implicate 
there  must  always  be  under  an  all-pervading  Law  of 
Thought  which  has  not  yet  been  named,  but  which 
may  be  called  tentatively  the  law  of  Homogeneous 
Counter-relativity.  The  title,  one  hopes,  is  sufficiently 


158  The  Interpretation  of  Propositions. 

technical-looking  :  though  cumbrous,  it  is  descriptive. 
The  law  itself  is  simple,  and  may  be  thus  stated  and 
explained. 


The  Law  of  Homogeneous  Counter-relativity. 

Every  positive  in  thought  has  a  contrapositive, 
and  the  positive  and  contrapositive  are  of  the 
same  kind. 

The  first  clause  of  our  law  corresponds  with  Dr. 
Bain's  law  of  Discrimination  or  Relativity :  it  is, 
indeed,  an  expansion  and  completion  of  that  law. 
Nothing  is  known  absolutely  or  in  isolation  ;  the 
various  items  of  our  knowledge  are  inter-relative ; 
everything  is  known  by  distinction  from  other  things. 
Light  is  known  as  the  opposite  of  darkness,  poverty  of 
riches,  freedom  of  slavery,  in  of  out ;  each  shade  of 
colour  by  contrast  to  other  shades.  What  Dr.  Bain 
lays  stress  upon  is  the  element  of  difference  in  this 
inter-relativity.  He  bases  this  law  of  our  knowledge 
on  the  fundamental  law  of  our  sensibility  that  change 
of  impression  is  necessary  to  consciousness.  A  long 
continuance  of  any  unvaried  impression  results  in 
insensibility  to  it.  We  have  seen  instances  of  this  in 
illustrating  the  maxim  that  custom  blunts  sensibility 
(p.  74).  Poets  have  been  beforehand  with  philosophers 
in  formulating  this  principle.  It  is  expressed  with  the 
greatest  precision  by  Barbour  in  his  poem  of  "  The 
Bruce,"  where  he  insists  that  men  who  have  never 
known  slavery  do  not  know  what  freedom  is. 

Thus  contrar  thingis  evermare 
Discoverings  of  t'  other  are. 


The  Counter-Implication  of  Propositions.         159 

Since,  then,  everything  that  comes  within  our  con- 
sciousness comes  as  a  change  or  transition  from 
something  else,  it  results  that  our  knowledge  is  counter- 
relative.  It  is  in  the  clash  or  conflict  of  impressions 
that  knowledge  emerges  :  every  item  of  knowledge  has 
its  illuminating  foil,  by  which  it  is  revealed,  over  against 
which  it  is  defined.  Every  positive  in  thought  has  its 
contrapositive. 

So  much  for  the  element  of  difference.  But  this  is 
not  the  whole  of  the  inter-relativity.  The  Hegelians 
rightly  lay  stress  on  the  common  likeness  that  connects 
the  opposed  items  of  knowledge. 

"  Thought  is  not  only  distinction ;  it  is,  at  the  same  time, 
relation^  If  it  marks  off  one  thing  from  another,  it,  at  the 
same  time,  connects  one  thing  with  another.  Nor  can  either  of 
these  functions  of  thought  be  separated  from  the  other :  as 
Aristotle  himself  said,  the  knowledge  of  opposites  is  one.  A 
thing  which  has  nothing  to  distinguish  it  is  unthinkable,  but 
equally  unthinkable  is  a  thing  which  is  so  separated  from  all 
other  things  as  to  have  no  community  with  them.  If  then  the 


1  It  is  significant  of  the  unsuitableness  of  the  vague  unqualified 
word  Relativity  to  express  a  logical  distinction  that  Dr.  Bain  calls 
his  law  the  Law  of  Relativity  simply,  having  regard  to  the  relation 
of  difference,  i.e.,  to  Counter-Relativity,  while  Dr.  Caird  applies 
the  name  Relativity  simply  to  the  relation  of  likeness,  i.e.,  to  Co- 
relativity.  It  is  with  a  view  to  taking  both  forms  of  relation 
into  account  that  I  name  our  law  the  Law  of  Homogeneous 
Counter-relativity.  The  Protagorean  Law  of  Relativity  has 
regard  to  yet  another  relation,  the  relation  of  knowledge 
to  the  knowing  mind:  these  other  logical  laws  are  of  relations 
among  the  various  items  of  knowledge.  Aristotle's  category  of 
Relation  is  a  fourth  kind  of  relation  not  to  be  confused  with  the 
others.  "  Father — son,"  "  uncle — nephew,"  "  slave — master,"  are 
relata  in  Aristotle's  sense:  "father,"  "uncle"  are  homogeneous 
counter-relatives,  varieties  of  kinship ;  so  "  slave,"  "  freeman  "  are 
counter-relatives  in  social  status. 


160  The  Interpretation  of  Propositions. 

law  of  contradiction  be  taken  as  asserting  the  self-identity  of 
things  or  thoughts  in  a  sense  that  excludes  their  community — in 
other  words,  if  it  be  not  taken  as  limited  by  another  law  which 
asserts  the  relativity  of  the  things  or  thoughts  distinguished — it 
involves  a  false  abstraction.  ...  If,  then,  the  world,  as  an  intelli- 
gible world,  is  a  world  of  distinction,  differentiation,  individuality, 
it  is  equally  true  that  in  it  as  an  intelligible  world  there  are  no 
absolute  separations  or  oppositions,  no  antagonisms  which  cannot 
be  reconciled."1 

In  the  penultimate  sentence  of  this  quotation  Dr. 
Caird  differentiates  his  theory  against  a  Logical  counter- 
theory  of  the  Law  of  Identity,  and  in  the  last  sentence 
against  an  Ethical  counter-theory :  but  the  point  here 
is  that  he  insists  on  the  relation  of  likeness  among 
opposites.  Every  impression  felt  is  felt  as  a  change 
or  transition  from  something  else :  but  it  is  a  variation 
of  the  same  impression — the  something  else,  the 
contrapositive,  is  not  entirely  different.  Change 
itself  is  felt  as  the  opposite  of  sameness,  difference 
of  likeness,  and  likeness  of  difference.  We  do  not 
differentiate  our  impression  against  the  whole  world, 
as  it  were,  but  against  something  nearly  akin  to  it — 
upon  some  common  ground.  The  positive  and  the 
contrapositive  are  of  the  same  kind. 

Let  us  surprise  ourselves  in  the  act  of  thinking  and 
we  shall  find  that  our  thoughts  obey  this  law.  We 
take  note,  say,  of  the  colour  of  the  book  before  us : 
we  differentiate  it  against  some  other  colour  actually 
before  us  in  our  field  of  vision  or  imagined  in  our 
minds.  Let  us  think  of  the  blackboard  as  black :  the 
blackness  is  defined  against  the  whiteness  of  the 
figures  chalked  or  chalkable  upon  it,  or  against  the 
colour  of  the  adjacent  wall.  Let  us  think  of  a  man  as 

1  Dr.  Caird's  Hegel,  p.  134. 


The  Counter-Implication  of  Propositions.         161 

a  soldier ;  the  opposite  in  our  minds  is  not  the  colour 
of  his  hair,  or  his  height,  or  his  birthplace,  or  his 
nationality,  but  some  other  profession — soldier,  sailor, 
tinker,  tailor.  It  is  always  by  means  of  some  contra- 
positive  that  we  make  the  object  of  our  thoughts 
definite  ;  it  is  not  necessarily  always  the  same  opposite, 
but  against  whatever  opposite  it  is,  they  are  always 
homogeneous.  One  colour  is  contradistinguished 
from  another  colour,  one  shade  from  another  shade : 
colour  may  be  contradistinguished  from  shape,  but  it 
is  within  the  common  genus  of  sensible  qualities. 

A  curious  confirmation  of  this  law  of  our  thinking 
has  been  pointed  out  by  Mr.  Carl  Abel.1  In  Egyptian 
hieroglyphics,  the  oldest  extant  language,  we  find,  he 
says,  a  large  number  of  symbols  with  two  meanings, 
the  one  the  exact  opposite  of  the  other.  Thus  the 
same  symbol  represents  strong  and  weak;  above — below ; 
with — without ;  for— against.  This  is  what  the  Hege- 
lians mean  by  the  reconciliation  of  antagonisms  in 
higher  unities.  They  do  not  mean  that  black  is  white, 
but  only  that  black  and  white  have  something  in 
common — they  are  both  colours. 

I  have  said  that  this  law  of  Homogeneous  Counter- 
relativity  has  not  been  recognised  by  logicians.  This, 
however,  is  only  to  say  that  it  has  not  been  explicitly 
formulated  and  named,  as  not  being  required  for 
Syllogism ;  a  law  so  all-pervading  could  not  escape 
recognition,  tacit  or  express.  And  accordingly  we 
find  that  it  is  practically  assumed  in  Definition  :  it  is 
really  the  basis  of  definition  per  genus  et  differentiam. 
When  we  wish  to  have  a  definite  conception  of 
anything,  to  apprehend  what  it  is,  we  place  it  in  some 

1  See  article  on  Counter-Sense,  Contemporary  Review,  April, 
1884. 

II 


1 6?  The  Interpretations  of  Propositions. 

genus  and  distinguish  it  from  species  of  the  same.  In 
fact  our  law  might  be  called  the  Law  of  Specification  : 
in  obeying  the  logical  law  of  what  we  ought  to  do  with 
a  view  to  clear  thinking,  we  are  only  doing  with 
exactness  and  conscious  method  what  we  all  do  and 
cannot  help  doing  with  more  or  less  definiteness  in  our 
ordinary  thinking. 

It  is  thus  seen  that  logicians  conform  to  this  law 
when  they  are  not  occupied  with  the  narrow  considera- 
tions proper  to  Syllogism.  And  another  unconscious 
recognition  of  it  maybe  found  in  most  logical  text-books. 
Theoretically  the  not- A  of  the  Law  of  Contradiction  — 
(A  is  not  not-A) — is  an  infinite  term.  It  stands  for 
everything  but  A.  This  is  all  that  needs  to  be  assumed 
for  Conversion  and  Syllogism.  But  take  the  examples 
given  of  the  Formal  Obverse  or  Permutation,  "  All  men 
are  fallible ".  Most  authorities  would  give  as  the 
Formal  Obverse  of  this,  "No  men  are  infallible". 
But,  strictly  speaking,  "  infallible  "  is  of  more  limited 
and  definite  signification  than  not-fallible.  Not-fallible, 
other  than  fallible,  is  brown,  black,  chair,  table,  and 
every  other  nameable  thing  except  fallible.  Thus  in 
Obversion  and  Conversion  by  Contraposition,  the 
homogeneity  of  the  negative  term  is  tacitly  assumed  ; 
it  is  assumed  that  A  and  not-A  are  of  the  same  kind. 

Now  to  apply  this  Law  of  our  Thought  to  the  inter- 
pretation of  propositions.  Whenever  a  proposition  is 
uttered  we  are  entitled  to  infer  at  once  (or  immediately] 
that  the  speaker  has  in  his  mind  some  counter-proposi- 
tion, in  which  what  is  overtly  asserted  of  the  ostensible 
subject  is  covertly  denied  of  another  subject.  And  we 
must  know  what  this  counter-proposition,  the  counter- 
implicate  is,  before  we  can  fully  and  clearly  understand 


The  Counter- Implication  of  Propositions.         163 

Tiis  meaning.  But  inasmuch  as  any  positive  may  have 
more  than  one  contrapositive,  we  cannot  tell  immedi- 
ately or  without  some  knowledge  of  the  circumstances 
or  context,  what  the  precise  counter-implicate  is.  The 
peculiar  fallacy  incident  to  this  mode  of  interpretation 
is,  knowing  that  there  must  be  some  counter-implicate, 
to  jump  rashly  or  unwarily  to  the  conclusion  that  it  is 
some  definite  one. 

Dr.  Bain  applies  the  term  Material  Obverse  to  the 
form,  Not-S  is  not  P,  as  distinguished  from  the  form 
S  is  not  not-P,  which  he  calls  the  Formal  Obverse,  on 
the  ground  that  we  can  infer  the  Predicate-contrapositive 
at  once  from  the  form,  whereas  we  cannot  tell  the 
Subject-contrapositive  without  an  examination  of  the 
matter.  But  in  truth  we  cannot  tell  either  Predicate- 
contrapositive  or  Subject-contrapositive  as  it  is  in  the 
mind  of  the  speaker  from  the  bare  utterance.  We  can 
only  tell  that  if  he  has  in  his  mind  a  proposition 
definitely  analysed  into  subject  and  predicate,  he  must 
have  contrapositives  in  his  mind  of  both,  and  that  they 
must  be  homogeneous.  Let  a  man  say,  "  This  book 
is  a  quarto".  For  all  that  we  know  he  may  mean 
that  it  is  not  a  folio  or  that  it  is  not  an  octavo :  we 
only  know  for  certain,  under  the  law  of  Homogeneous 
Counter-relativity,  that  he  means  some  definite  other 
size.  Under  the  same  law,  we  know  that  he  has  a 
homogeneous  contrapositive  of  the  subject,  a  subject 
that  admits  of  the  same  predicate,  some  other  book 
in  short.  What  the  particular  book  is  we  do  not 
know. 

It  would  however  be  a  waste  of  ingenuity  to  dwell 
upon  the  manipulation  of  formulas  founded  on  this  law. 
The  practical  concern  is  to  know  that  for  the  interpre- 
tation of  a  proposition,  a  knowledge  of  the  counter- 


164  The  Interpretation  of  Propositions. 

implicate,  a  knowledge  of  what  it  is  meant  to  deny,  ia 
essential. 

The  manipulation  of  formulae,  indeed,  has  its  own 
special  snare.  We  are  apt  to  look  for  the  counterparts 
of  them  in  the  grammatical  forms  of  common  speech. 
Thus,  it  might  seem  to  be  a  fair  application  of  our  law 
to  infer  from  the  sentence,  "Wheat  is  dear,"  that  the 
speaker  had  in  his  mind  that  Oats  or  Sugar  or  Shirting 
or  some  other  commodity  is  cheap.  But  this  would  be 
a  rash  conclusion.  The  speaker  may  mean  this,  but 
he  may  also  mean  that  wheat  is  dear  now  as  compared 
with  some  other  time :  that  is,  the  Positive  subject  in 
his  mind  may  be  "  Wheat  as  now,"  and  the  Contra- 
positive  "  Wheat  as  then  ".  So  a  man  may  say,  "All 
men  are  mortal,"  meaning  that  the  angels  never  taste 
death,  "  angels  "  being  the  contrapositive  of  his  subject 
"  men  ".  Or  he  may  mean  merely  that  mortality  is  a 
sad  thing,  his  positive  subject  being  men  as  they  are, 
and  his  contrapositive  men  as  he  desires  them  to  be. 
Or  his  emphasis  may  be  upon  the  all,  and  he  may 
mean  only  to  deny  that  some  one  man  in  his  mind 
(Mr.  Gladstone,  for  example)  is  immortal.  It  would 
be  misleading,  therefore,  to  prescribe  propositions  as 
exercises  in  Material  Obversion,  if  we  give  that  name 
to  the  explicit  expression  of  the  Contrapositive  Subject : 
it  is  only  from  the  context  that  we  can  tell  what  this 
is.  The  man  who  wishes  to  be  clearly  understood 
gives  us  this  information,  as  when  the  epigrammatist 
said  :  "  We  are  all  fallible — even  the  youngest  of  us  ". 

But  the  chief  practical  value  of  the  law  is  as  a  guide 
in  studying  the  development  of  opinions.  Every 
doctrine  ever  put  forward  has  been  put  forward  in 
opposition  to  a  previous  doctrine  on  the  same  subject. 
Until  we  know  what  the  opposed  doctrine  is,  we  cannot 


The  Counter-Implication  of  Propositions.          165 

be  certain  of  the  meaning.  We  cannot  gather  it  with 
precision  from  a  mere  study  of  the  grammatical  or 
even  (in  the  narrow  sense  of  the  word)  the  logical  con- 
tent of  the  words  used.  This  is  because  the  framers 
of  doctrines  have  not  always  been  careful  to  put  them 
in  a  clear  form  of  subject  and  predicate,  while  their 
impugners  have  not  moulded  their  denial  exactly  on 
the  language  of  the  original.  No  doubt  it  would  have 
been  more  conducive  to  clearness  if  they  had  done  so. 
But  they  have  not,  and  we  must  take  them  as  they 
are.  Thus  we  have  seen  that  the  Hegelian  doctrine  of 
Relativity  is  directed  against  certain  other  doctrines  in 
Logic  and  in  Ethics ;  that  Ultra-Nominalism  is  a  con- 
tradiction of  a  certain  form  of  Ultra-Realism  ;  and  that 
various  theories  of  Predication  each  has  a  backward 
look  at  some  predecessor. 

I  quote  from  Mr.  A.  B.  Walkley  a  very  happy  appli- 
cation of  this  principle  of  interpretation  : — 

"  It  has  always  been  a  matter  for  speculation  why  so  sagacious 
an  observer  as  Diderot  should  have  formulated  the  wild  paradox 
that  the  greatest  actor  is  he  who  feels  his  part  the  least.  Mr. 
Archer's  bibliographical  research  has  solved  this  riddle.  Diderot's 
paradox  was  a  protest  against  a  still  wilder  one.  It  seems  that  a 
previous  eighteenth  century  writer  on  the  stage,  a  certain  Saint- 
Albine,  had  advanced  the  fantastic  propositions  that  none  but  a 
magnanimous  man  can  act  magnanimity,  that  only  lovers  can 
do  justice  to  a  love  scene,  and  kindred  assertions  that  read  like 
variations  on  the  familiar  '  Who  drives  fat  oxen  must  himself  be 
fat '.  Diderot  saw  the  absurdity  of  this  ;  he  saw  also  the  essentially 
artificial  nature  of  the  French  tragedy  and  comedy  of  his  own  day; 
and  he  hastily  took  up  the  position  which  Mr.  Archer  has  now 
shown  to  be  untenable." 

This  instance  illustrates  another  principle  that  has 
to  be  borne  in  mind  in  the  interpretation  of  doctrines 
from  their  historical  context  of  counter-implication. 


1 66  The  Interpretation  of  Propositions. 

This  is  the  tendency  that  men  have  to  put  doctrines  IIT 
too  universal  a  form,  and  to  oppose  universal  to  uni- 
versal, that  is,  to  deny  with  the  flat  contrary,  the  very 
reverse,  when  the  more  humble  contradictory  is  all 
that  the  truth  admits  of.  If  a  name  is  wanted  for  this 
tendency,  it  might  be  called  the  tendency  to  Over- 
Contradiction.  Between  "  All  are  "  and  "  None  are," 
the  sober  truth  often  is  that  "  Some  are  "  and  "  Some 
are  not,"  and  the  process  of  evolution  has  often  con- 
sisted in  the  substitution  of  these  sober  forms  for  their 
more  violent  predecessors. 


PART    IV. 

THE  INTERDEPENDENCE  OF  PROPOSI- 
TIONS.—MEDIATE  INFERENCE.— 
SYLLOGISM. 


CHAPTER  I. 
THE  SYLLOGISM. 

WE  have  already  defined  mediate  inference  as  the 
derivation  of  a  conclusion  from  more  than  one  propo- 
sition. The  type  or  form  of  a  mediate  inference  fully 
expressed  consists  of  three  propositions  so  related  that 
one  of  them  is  involved  or  implied  in  the  other  two. 

Distraction  is  exhausting. 
Modern  life  is  full  of  distraction. 
.'.  Modern  life  is  exhausting. 

We  say  nothing  of  the  truth  of  these  propositions. 
I  purposely  choose  questionable  ones.  But  do  they 
hang  together  ?  If  you  admit  the  first  two,  are  you 
bound  in  consistency  to  admit  the  third  ?  Is  the 
truth  of  the  conclusion  a  necessary  consequence  of 
the  truth  of  the  premisses  ?  If  so,  it  is  a  valid 
mediate  inference  from  them. 
(167) 


1 68  The  Interdependence  of  Propositions. 

When  one  of  the  two  premisses  is  more  general  than 
the  conclusion,  the  argument  is  said  to  be  Deductive. 
You  lead  down  from  the  more  general  to  the  less 
general.  The  general  proposition  is  called  the  Major 
Premiss,  or  Grounding  Proposition,  or  Sumption  :  the 
other  premiss  the  Minor,  or  Applying  Proposition,  or 
Subsumption. 

Undue  haste  makes  waste. 
This  is  a  case  of  undue  hasting- 
.*.  It  is  a  case  of  undue  wasting. 

We  may,  and  constantly  do,  apply  principles  and 
draw  conclusions  in  this  way  without  making  any 
formal  analysis  of  the  propositions.  Indeed  we  reason 
mediately  and  deductively  whenever  we  make  any 
application  of  previous  knowledge,  although  the 
process  is  not  expressed  in  propositions  at  all  and  is 
performed  so  rapidly  that  we  are  not  conscious  of  the 
steps. 

For  example,  I  enter  a  room,  see  a  book,  open  it 
and  begin  to  read.  I  want  to  make  a  note  of  some- 
thing :  I  look  round,  see  a  paper  case,  open  it,  take  a 
sheet  of  paper  and  a  pen,  dip  the  pen  in  the  ink  and 
proceed  to  write.  In  the  course  of  all  this,  I  act  upon 
certain  inferences  which  might  be  drawn  out  in  the 
form  of  Syllogisms.  First,  in  virtue  of  previous 
knowledge  I  recognise  what  lies  before  me  as  a  book. 
The  process  by  which  I  reach  the  conclusion,  though 
it  passes  in  a  flash,  might  be  analysed  and  expressed 
in  propositions. 

Whatever  presents  certain  outward  appearances, 

contains  readable  print. 
This  presents  such  appearances. 
V  It  contains  readable  print. 


The  Syllogism.  169 

So  with  the  paper  case,  and  the  pen,  and  the  ink.  I 
infer  from  peculiar  appearances  that  what  I  see  contains 
paper,  that  the  liquid  will  make  a  black  mark  on  the 
white  sheet,  and  so  forth. 

We  are  constantly  in  daily  life  subsuming  particulars 
under  known  universals  in  this  way.  "  Whatever  has 
certain  visible  properties,  has  certain  other  properties  : 
this  has  the  visible  ones  :  therefore,  it  has  the  others" 
is  a  form  of  reasoning  constantly  latent  in  our  minds. 
The  Syllogism  may  be  regarded  as  the  explicit 
expression  of  this  type  of  deductive  reasoning ;  that  is, 
as  the  analysis  and  formal  expression  of  this  every-day 
process  of  applying  known  universals  to  particular 
cases.  Thus  viewed  it  is  simply  the  analysis  of  a 
mental  process,  as  a  psychological  fact ;  the  analysis 
of  the  procedure  of  all  men  when  they  reason  from 
signs  ;  the  analysis  of  the  kind  of  assumptions  they 
make  when  they  apply  knowledge  to  particular  cases. 
The  assumptions  may  be  warranted,  or  they  may  not: 
but  as  a  matter  of  fact  the  individual  who  makes  the 
confident  inference  has  such  assumptions  and  sub- 
sumptions  latent  in  his  mind. 

But  practically  viewed,  that  is  logically  viewed,  if 
you  regard  Logic  as  a  practical  science,  the  Syllogism 
is  a  contrivance  to  assist  the  correct  performance  of 
reasoning  together  or  syllogising  in  difficult  cases.  It 
applies  not  to  mental  processes  but  to  results  of  such 
expressed  in  words,  that  is,  to  propositions.  Where 
the  Syllogism  comes  in  as  a  useful  form  is  when 
certain  propositions  are  delivered  to  you  ab  extra  as 
containing  a  certain  conclusion  ;  and  the  connexion  is 
not  apparent.  These  propositions  are  analysed  and 
thrown  into  a  form  in  which  it  is  at  once  apparent 
whether  the  alleged  connexion  exists.  This  form  is 


1 70  The  Interdependence  of  Propositions. 

the  Syllogism  :  it   is,   in   effect,   an   analysis  of  given 
arguments. 

It  was  as  a  practical  engine  or  organon  that  it  was 
invented  by  Aristotle,  an  organon  for  the  syllogising  of 
admissions  in  Dialectic.  The  germ  of  the  invention 
was  the  analysis  of  propositions  into  terms.  The 
syllogism  was  conceived  by  Aristotle  as  a  reasoning 
together  of  terms.  His  prime  discovery  was  that 
whenever  two  propositions  necessarily  contain  or  imply 
a  conclusion,  they  have  a  common  term,  that  is,  only 
three  terms  between  them :  that  the  other  two  terms 
which  differ  in  each  are  the  terms  of  the  conclusion  ; 
and  that  the  relation  asserted  in  the  conclusion  between 
its  two  terms  is  a  necessary  consequence  of  their 
relations  with  the  third  term  as  declared  in  the 
premisses. 

Such  was  Aristotle's  conception  of  the  Syllogism 
and  such  it  has  remained  in  Logic.  It  is  still,  strictly 
speaking,  a  syllogism  of  terms :  of  propositions  only 
secondarily  and  after  they  have  been  analysed.  The 
conclusion  is  conceived  analytically  as  a  relation 
between  two  terms.  In  how  many  ways  may  this 
relation  be  established  through  a  third  term  ?  The 
various  moods  and  figures  of  the  Syllogism  give  the 
answer  to  that  question. 

The  use  of  the  very  abstract  word  "  relation  "  makes 
the  problem  appear  much  more  difficult  than  it  really 
is.  The  great  charm  of  Aristotle's  Syllogism  is  its 
simplicity.  The  assertion  of  the  conclusion  is  reduced 
to  its  simplest  possible  kind,  a  relation  of  inclusion  or 
exclusion,  contained  or  not  contained.  To  show  that 
the  one  term  is  or  is  not  contained  in  the  other  we 
have  only  to  find  a  third  which  contains  the  one  and  is- 
contained  or  not  contained  in  the  other. 


The  Syllogism.  171 

The  practical  difficulties,  of  course,  consist  in  the 
reduction  of  the  conclusions  and  arguments  of  common 
speech  to  definite  terms  thus  simply  related.  Once 
they  are  so  reduced,  their  independence  or  the 
opposite  is  obvious.  Therein  lies  the  virtue  of  the 
Syllogism. 

Before  proceeding  to  show  in  how  many  ways  two 
terms  may  be  Syllogised  through  a  third,  we  must  have 
technical  names  for  the  elements. 

The  third  term  is  called  the  Middle  (M)  (TO  fteVov) : 
the  other  two  the  Extremes  (<x/cpa). 

The  Extremes  are  the  Subject  (S)  and  the  Predicate 
(P)  of  the  conclusion. 

In  an  affirmative  proposition  (the  normal  form)  S 
is  contained  in  P:  hence  P  is  called  the  Major1  term 
(TO  /xet£ov),  and  S  the  Minor  (TO  IXarrov),  being  respec- 
tively larger  and  smaller  in  extension.  All  difficulty 
about  the  names  disappears  if  we  remember  that  in 
bestowing  them  we  start  from  the  conclusion.  That 
was  the  problem  (Trpo/^V/^a)  or  thesis  in  dialectic,  the 
question  in  dispute. 

The  two  Premisses,  or  propositions  giving  the 
relations  between  the  two  Extremes  and  the  Middle, 
are  named  on  an  equally  simple  ground. 

One  of  them  gives  the  relation  between  the 
Minor  Term,  S,  and  the  Middle,  M.  S,  All  or  Some, 
is  or  is  not  in  M.  This  is  called  the  Minor 
Premiss. 

The  other  gives  the   relation    between   the   Major 


1  Aristotle  calls  the  Major  the  First  (rb  irpurov)  and  the  Minor 
the  Last  (rb  fvxarov),  probably  because  that  was  their  order  in  the 
conclusion  when  stated  in  his  most  usual  form,  "  P  is  predicated 
of  S,"  or  "  P  belongs  to  S  ". 


172  The  Interdependence  of  Propositions. 

Term  and  the  Middle.     M,  All  or  Some,  is  or  is  not  in 
P.     This  is  called  the  Major  Premiss.1 

1When  we  speak  of  the  Minor  or  the  Major  simply,  the 
reference  is  to  the  terms.  To  avoid  a  confusion  into  which 
beginners  are  apt  to  stumble,  and  at  the  same  time  to  emphasise 
the  origin  of  the  names,  the  Premisses  might  be  spoken  of  at  first 
as  the  Minor's  Premiss  and  the  Major's  Premiss.  It  was  only  in 
the  Middle  Ages  when  the  origin  of  the  Syllogism  had  been  for- 
gotten, that  the  idea  arose  that  the  terms  were  called  Major  and 
Minor  because  they  occurred  in  the  Major  and  the  Minor 
Premiss  respectively. 


CHAPTER  II. 

FIGURES  AND  MOODS  OF  THE  SYLLOGISM. 
I. — THE  FIRST  FIGURE. 

THE  forms  (technically  called  Moods,  i.e.,  modes)  of 
the  First  Figure  are  founded  on  the  simplest  relations 
with  the  Middle  that  will  yield  or  that  necessarily 
involve  the  disputed  relation  between  the  Extremes. 

The  simplest  type  is  stated  by  Aristotle  as  follows : 
"When  three  terms  are  so  related  that  the  last  (the 
Minor)  is  wholly  in  the  Middle,  and  the  Middle  wholly 
either  in  or  not  in  the  first  (the  Major)  there  must  be 
a  perfect  syllogism  of  the  Extremes ". l 

When  the  Minor  is  partly  in  the  Middle,  the 
Syllogism  holds  equally  good.  Thus  there  are  four 
possible  ways  in  which  two  terms  (opot,  plane  enclo- 
sures) may  be  connected  or  disconnected  through  a 
third.  Thev  are  usually  represented  by  circles  as 
being  the  neatest  of  figures,  but  any  enclosing  outline 
answers  the  purpose,  and  the  rougher  and  more 
irregular  it  is  the  more  truly  will  it  represent  the 
extension  of  a  word. 


1  "OTOJ/  odv  opot  rpets  OVTWS  exa>(rt  ""P^s  aAA^Aoi/s  Sxrre  r'bv 
eV  o\cf  flvai  T<p  fj.€<rcj),  Kal  rbv  /j.t(rov  ev  o\q>  T<£  Trpury  j)  tlvai  T)  /*?? 
6?i/cu,  avdyia]  rcav  &Kpcai/  elvai  <rv\\oyi<rjnbv  reAeioz/.    (Anal.  Prior.,  i.  4.) 

(T73) 


174 


The  Interdependence  of  Propositions. 


Conclusion  A. 
All  M  is  in  P. 
All  S  is  in  M. 
All  S  is  in  P. 

Conclusion  E. 
No  M  is  in  P. 
All  S  is  in  M. 
No  S  is  in  P. 

Conclusion  I. 
All  M  is  in  P. 
Some  S  is  in  M. 
Some  S  is  in  P. 


Conclusion  O. 
No  M  is  in  P. 
Some  S  is  in  M. 
Some  Sis  not  in  P. 


These  four  forms  constitute  what  are  known  as  the 
moods  of  the  First  Figure  of  the  Syllogism.  Seeing 
that  all  propositions  may  be  reduced  to  one  or  other 
of  the  four  forms,  A,  E,  I,  or  O,  we  have  in  these 
premisses  abstract  types  of  every  possible  valid  argu- 
ment from  general  principles.  It  is  all  the  same 
whatever  be  the  matter  of  the  proposition.  Whether 
the  subject  of  debate  is  mathematical,  physical,  social, 
or  political,  once  premisses  in  these  forms  are  con- 
ceded, the  conclusion  follows  irresistibly,  ex  vi  fcrmce, 
•ax  necessitate  forma.  If  an  argument  can  be  analysed 


Figures  and  Moods  of  the  Syllogism.  175 

into  these  forms,  and  you  admit  its  propositions,  you 
are  bound  in  consistency  to  admit  the  conclusion — 
unless  you  are  prepared  to  deny  that  if  one  thing  is  in 
another  and  that  other  in  a  third,  the  first  is  in  the 
third,  or  if  one  thing  is  in  another  and  that  other 
wholly  outside  a  third,  the  first  is  also  outside  the 
third. 

This  is  called  the  Axiom  of  Syllogism.  The  most 
common  form  of  it  in  Logic  is  that  known  as  the 
Dictum,  or  Regula  de  Omni  et  Nullo :  "Whatever  is 
predicated  of  All  or  None  of  a  term,  is  predicated  of 
whatever  is  contained  in  that  term".  It  has  been 
expressed  with  many  little  variations,  and  there  has 
been  a  good  deal  of  discussion  as  to  the  best  way  of 
expressing  it,  the  relativity  of  the  word  best  being  often 
left  out  of  sight.  Best  for  what  purpose  ?  Practically 
that  form  is  the  best  which  best  commands  general 
assent,  and  for  this  purpose  there  is  little  to  choose 
between  various  ways  of  expressing  it.  To  make  it 
easy  and  obvious  it  is  perhaps  best  to  have  two 
separate  forms,  one  for  affirmative  conclusions  and 
one  for  negative.  Thus :  "  Whatever  is  affirmed  of 
all  M,  is  affirmed  of  whatever  is  contained  in  M  :  and 
whatever  is  denied  of  all  M,  is  denied  of  whatever  is 
contained  in  M  ".  The  only  advantage  of  including 
the  two  forms  in  one  expression,  is  compendious 
neatness.  "  A  part  of  a  part  is  a  part  of  the  whole,"  is 
a  neat  form,  it  being  understood  that  an  individual  or 
a  species  is  part  of  a  genus.  "What  is  said  of  a 
whole,  is  said  of  every  one  of  its  parts,"  is  really  a 
sufficient  statement  of  the  principle  :  the  whole  being 
the  Middle  Term,  and  the  Minor  being  a  part  of  it, 
the  Major  is  predicable  of  the  Minor  afiirmatively  or 
negatively  if  it  is  predicable  similarly  of  the  Middle. 


176  The  Interdependence  of  Propositions. 

This  Axiom,  as  the  name  imports,  is  indemonstrable. 
As  Aristotle  pointed  out  in  the  case  of  the  Axiom  of 
Contradiction,  it  can  be  vindicated,  if  challenged,  only 
by  reducing  the  challenger  to  a  practical  absurdity. 
You  can  no  more  deny  it  than  you  can  deny  that  if  a 
leaf  is  in  a  book  and  the  book  is  in  your  pocket,  the 
leaf  is  in  your  pocket.  If  you  say  that  you  have  a 
sovereign  in  your  purse  and  your  purse  is  in  your 
pocket,  and  yet  that  the  sovereign  is  not  in  your 
pocket :  will  you  give  me  what  is  in  your  pocket  for 
the  value  of  the  purse  ? 


II. — THE  MINOR  FIGURES  OF  THE  SYLLOGISM,  AND 
THEIR  REDUCTION  TO  THE  FIRST. 

The  word  Figure  (crx^a)  applies  to  the  form  or 
figure  of  the  premisses,  that  is,  the  order  of  the  terms 
in  the  statement  of  the  premisses,  when  the  Major 
Premiss  is  put  first,  and  the  Minor  second. 

In  the  First  Figure  the  order  is 

M  P 
S  M. 

But  there  are  three  other  possible  orders  or  figures, 
namely : — 

Fig.  ii.  Fig.  iii.  Fig.  iv. 

PM  MP  PM 

SM  MS  MS. 

It  results  from  the  doctrines  of  Conversion  that 
valid  arguments  may  be  stated  in  these  forms, 
inasmuch  as  a  proposition  in  one  order  of  terms  may 
be  equivalent  to  a  proposition  in  another.  Thus  No 


Figures  and  Moods  of  the  Syllogism.  177 

M  is  in  P  is  convertible  with  No  P  is  in  M  :  con- 
sequently the  argument 

No  P  is  in  M 
All  S  is  in  M, 

in  the  Second  Figure  is  as  much  valid  as  when  it  is 
stated  in  the  First — 

No  M  is  in  P 
All  S  is  in  M. 

Similarly,  since  All  M  is  in  S  is  convertible  into  Some 
S  is  in  M,  the  following  arguments  are  equally 
valid : — 

Fig.  iii.  Fig.  i. 

All  M  is  in  P  All  M  is  in  P 

All  M  is  in  S  Some  S  is  in  M. 

Using  both  the  above  Converses  in  place  of  their 
Convertends,  we  have — 

Fig.  iv.  Fig.  i. 

No  P  is  in  M  No  M  is  in  P 

All  M  is  in  S  Some  S  is  in  M. 

It  can  be  demonstrated  (we  shall  see  presently  how) 
that  altogether  there  are  possible  four  valid  forms  or 
moods  of  the  Second  Figure,  six  of  the  Third,  and  five 
of  the  Fourth.  An  ingenious  Mnemonic  of  these 
various  moods  and  their  reduction  to  the  First  Figure 
by  the  transposition  of  terms  and  premisses  has  come 
down  from  the  thirteenth  century.  The  first  line  names 
the  moods  of  the  First,  Normal,  or  Standard  Figure. 

12 


178  The  Interdependence  of  Propositions. 

BAr&ArA,  CE/ArEnt,  DArll,  FErlOgue  prioris ; 
CEsArE,  CAmEstrEs,  FEstlnO,  BArO^O,  secundae ; 
Tertia  DArA//I,  DlsAmls,  DA/Lrl,  FE/A//O«, 
BO^Ar^O,  FErljO^w,  habet ;  quarta  insuper  addit, 
BrAmAntIP,  CAmEnEs,  DImArls,  FEjA/0,  FrEsIsOn. 

The  vowels  in  the  names  of  the  Moods  indicate  the 
propositions  of  the  Syllogism  in  the  four  forms, 
A  E  I  O.  To  write  out  any  Mood  at  length  you  have 
only  to  remember  the  Figure,  and  transcribe  the  pro- 
positions in  the  order  of  Major  Premiss,  Minor  Premiss, 

PM 
and  Conclusion.     Thus,  the  Second  Figure  being  gj^ 

FEstlnO  is  written — 

No  P  is  in  M. 
Some  S  is  in  M. 
Some  S  is  not  in  P. 

PM 
The  Fourth   Figure  being  M§  DImArls  is 

Some  P  is  in  M. 
All  M  is  in  S. 
Some  S  is  in  P. 

The  initial  letter  in  a  Minor  Mood  indicates  that 
Mood  of  the  First  to  which  it  may  be  reduced.  Thus 
Festino  is  reduced  to  Ferio,  and  Dimaris  to  Darii.  In 
the  cases  of  Baroko  and  Bokardo,  B  indicates  that  you 
may  employ  Barbara  to  bring  any  impugner  to  con- 
fusion, as  shall  be  afterwards  explained. 

The  letters  s,  m,  and  /  are  also  significant.  Placed 
after  a  vowel,  s  indicates  that  the  proposition  has  to  be 
simply  converted.  Thus,  FEstlnO  : — 

No  P  is  in  M. 

Some  S  is  in  M. 

Some  S  is  not  in  P. 


Figures  and  Moods  of  the  Syllogism.  179 

Simply  convert  the  Major  Premiss,  and  you  get  FErlO, 
-of  the  First. 

No  M  is  in  P. 

Some  S  is  in  M. 

Some  S  is  not  in  P. 

m  (muta,  or  move)  indicates  that  the  premisses  have 
to  be  transposed.  Thus,  in  CAmEstrEs,  you  have  to 
transpose  the  premisses,  as  well  as  simply  convert  the 
Minor  Premiss  before  reaching  the  figure  of  CElAi-Ent. 

All  P  is  in  M  No  M  is  in  S 

No  S  is  in  M  All  P  is  in  M. 

From  this  it  follows  in  CE/ArEnt  that  No  P  is  in  S, 
and  this  simply  converted  yields  No  S  is  in  P. 

A  simple  transposition  of  the  premisses  in  DImArls 
of  the  Fourth 

Some  P  is  in  M 

All  M  is  in  S 

yields  the  premisses  of  DArll 

All  M  is  in  S 
Some  P  is  in  M, 

but  the  conclusion  Some  P  is  in  S  has  to  be  simply 
converted. 

Placed  after  a  vowel,  /  indicates  that  the  proposition 
has  to  be  converted  per  acddens.  Thus  in  FE/A^/O« 
of  the  Third  (MP,  MS) 

No  M  is  in  P 
All  M  is  in  S 
Some  S  is  not  in  P 

you  have  to  substitute  for  All  M  is  in  S  its  converse 
by  limitation  to  get  the  premisses  of  FE/IO. 


180  The  Interdependence  of  Propositions. 

Two  of  the  Minor  Moods,  Baroko  of  the  Second 
Figure,  and  Bokardo  of  the  Third,  cannot  be  reduced 
to  the  First  Figure  by  the  ordinary  processes  of  Conver- 
sion and  Transposition.  It  is  for  dealing  with  these 
intractable  moods  that  Contraposition  is  required. 
Thus  in  BArO^O  of  the  Second  (PM,  SM) 

All  P  is  in  M. 
Some  S  is  not  in  M. 

Substitute  for  the  Major  Premiss  its  Converse  by 
Contraposition,  and  for  the  Minor  its  Formal  Obverse 
or  Permutation,  and  you  have  FErlO  of  the  First, 
with  not-M  as  the  Middle. 

No  not-M  is  in  P. 
Some  S  is  in  not-M. 
Some  S  is  not  in  P. 

The  processes  might  be  indicated  by  the  Mnemonic 
FAcsOcO,  with  c  indicating  the  contraposition  of  the 
predicate  term  or  Formal  Obversion. 
The  reduction  of  BO&WO, 

Some  M  is  not  in  P 
All  M  is  in  S 
Some  S  is  not  in  P, 

is  somewhat  more  intricate.  It  may  be  indicated  by 
DOcsAmOsc.  You  substitute  for  the  Major  Premiss 
its  Converse  by  Contraposition,  transpose  the  Pre- 
misses, and  you  have  DArll. 

All  M  is  in  S. 
Some  not-P  is  in  M. 
Some  not-P  is  in  S. 


Figures  and  Moods  of  the  Syllogism.  181 

Convert  now  the  conclusion  by  Contraposition,  and 
you  have  Some  S  is  not  in  P. 

The  author  oi  the  Mnemonic  apparently  did  not 
recognise  Contraposition,  though  it  was  admitted  by 
Boethius;  and,  it  being  impossible  without  this  to 
demonstrate  the  validity  of  Baroko  and  Bokardo  by 
showing  them  to  be  equivalent  with  valid  moods  of 
the  First  Figure,  he  provided  for  their  demonstration 
by  the  special  process  known  as  Reductio  ad  absurdum. 
B  indicates  that  Barbara  is  the  medium. 

The  rationale  of  the  process  is  this.  It  is  an  imagi- 
nary opponent  that  you  reduce  to  an  absurdity  or  self- 
contradiction.  You  show  that  it  is  impossible  with 
consistency  to  admit  the  premisses  and  at  the  same 
time  deny  the  conclusion.  For,  let  this  be  done ;  let  it 
be  admitted  as  in  BArO&O  that, 

All  P  is  in  M 
Some  S  is  not  in  M, 

but  denied  that  Some  S  is  not  in  P.  The  denial  of  a 
proposition  implies  the  admission  of  its  Contradictory. 
If  it  is  not  true  that  Some  S  is  not  in  P,  it  must  be 
true  that  All  S  is  in  P.  Take  this  along  with  the 
admission  that  All  P  is  in  M,  and  you  have  a  syllogism 
in  BArAArA, 

All  P  is  in  M 
All  S  is  in  P, 

yielding  the  conclusion  All  S  is  in  M.  If  then  the 
original  conclusion  is  denied,  it  follows  that  All  S  is 
in  M.  But  this  contradicts  the  Minor  Premiss,  which 
has  been  admitted  to  be  true.  It  is  thus  shown  that 


1 82  The  Interdependence  of  Propositions. 

an  opponent  cannot  admit  the  premisses  and  deny  the 
conclusion  without  contradicting  himself. 

The  same  process  may  be  applied  to  Bokardo. 

Some  M  is  not  in  P. 
All  M  is  in  S. 
Some  S  is  not  in  P. 

Deny  the  conclusion,  and  you  must  admit  that  All 
S  is  in  P.  Syllogised  in  Barbara  with  All  M  is  in  S, 
this  yields  the  conclusion  that  All  M  is  in  P,  the 
contradictory  of  the  Major  Premiss. 

The  beginner  may  be  reminded  that  the  argument 
ad  absurdum  is  not  necessarily  confined  to  Baroko  and 
Bokardo.  It  is  applied  to  them  simply  because  they 
are  not  reducible  by  the  ordinary  processes  to  the  First 
Figure.  It  might  be  applied  with  equal  effect  to- 
other Moods,  DImArls,  e.g.,  of  the  Third. 

Some  M  is  in  P. 
All  M  is  in  S. 
Some  S  is  in  P. 

Let  Some  S  is  in  P  be  denied,  and  No  S  is  in  P  must 
be  admitted.  But  if  No  S  is  in  P  and  All  M  is  in  Sr 
it  follows  (in  Celarent)  that  No  M  is  in  P,  which  an 
opponent  cannot  hold  consistently  with  his  admission 
that  Some  M  is  in  P. 

The  beginner  sometimes  asks :  What  is  the  use  of 
reducing  the  Minor  Figures  to  the  First  ?  The  reason 
is  that  it  is  only  when  the  relations  between  the  terms 
are  stated  in  the  First  Figure  that  it  is  at  once  appa- 
rent whether  or  not  the  argument  is  valid  under  the 
Axiom  or  Dictum  de  Omni.  It  is  then  undeniably 
evident  that  if  the  Dictum  holds  the  argument  holds. 


Figures  and  Moods  of  the  Syllogism.  183 

And  if  the  Moods  of  the  First  Figure  hold,  their 
equivalents  in  the  other  Figures  must  hold  too. 

Aristotle  recognised  only  two  of  the  Minor  Figures, 
the  Second  and  Third,  and  thus  had  in  all  only  fourteen 
valid  moods. 

The  recognition  of  the  Fourth  Figure  is  attributed 
by  Averroes  to  Galen.  Averroes  himself  rejects  it  on 
the  ground  that  no  arguments  expressed  naturally, 
that  is,  in  accordance  with  common  usage,  fall  into 
that  form.  This  is  a  sufficient  reason  for  not  spending 
time  upon  it,  if  Logic  is  conceived  as  a  science  that 
has  a  bearing  upon  the  actual  practice  of  discussion  or 
discursive  thought.  And  this  was  probably  the  reason 
why  Aristotle  passed  it  over. 

If  however  the  Syllogism  of  Terms  is  to  be  com- 
pleted as  an  abstract  doctrine,  the  Fourth  Figure  must 
be  noticed  as  one  of  the  forms  of  premisses  that  contain 
the  required  relation  between  the  extremes.  There  is 
a  valid  syllogism  between  the  extremes  when  the 
relations  of  the  three  terms  are  as  staled  in  certain 
premisses  of  the  Fourth  Figure. 

III.— THE  SORITES. 
A  chain  of  Syllogisms  is  called  a  Sorites.     Thus  :  — 

All  A  is  in  B. 
All  B  is  in  C. 
All  C  is  in  D, 


All  X  is  in  Z. 
/.  All  A  is  in  Z. 

A    Minor    Premiss    can    thus    be   carried    through    a 


184  The  Interdependence  of  Propositions. 

series  of  Universal  Propositions  each  serving  in  turn 
as  a  Major  to  yield  a  conclusion  which  can  be  syllo- 
gised with  the  next.  Obviously  a  Sorites  may  contain 
one  particular  premiss,  provided  it  is  the  first ;  and 
one  universal  negative  premiss,  provided  it  is  the  last. 
A  particular  or  a  negative  at  any  other  point  in  the 
chain  is  an  insuperable  bar. 


CHAPTER  III. 

THE  DEMONSTRATION  OF  THE  SYLLOGISTIC  MOODS. 
—THE  CANONS  OF  THE  SYLLOGISM. 

How  do  we  know  that  the  nineteen  moods  are  the 
only  possible  forms  of  valid  syllogism  ? 

Aristotle  treated  this  as  being  self-evident  upon  trial 
and  simple  inspection  of  all  possible  forms  in  each  of 
his  three  Figures. 

Granted  the  parity  between  predication  and  position 
in  or  out  of  a  limited  enclosure  (term,  0/005),  it  is  a 
matter  of  the  simplest  possible  reasoning.  You  have 
three  such  terms  or  enclosures,  S,  P  and  M  ;  and  you 
are  given  the  relative  positions  of  two  of  them  to  the 
third  as  a  clue  to  their  relative  positions  to  one 
another.  Is  S  in  or  out  of  P,  and  is  it  wholly  in  or 
wholly  out  or  partly  in  or  partly  out  ?  You  know  how 
each  of  them  lies  towards  the  third  :  when  can  you 
tell  from  this  how  S  lies  towards  P  ? 

We  have  seen  that  when  M  is  wholly  in  or  out  of  P, 
and  S  wholly  or  partly  in  M,  S  is  wholly  or  partly  in 
or  out  of  P. 

Try  any  other  given  positions  in  the  First  Figure, 
and  you  find  that  you  cannot  tell  from  them  how  S 
lies  relatively  to  P.  Unless  the  Major  Premiss  is 
Universal,  that  is,  unless  M  lies  wholly  in  or  out  of  P, 
you  can  draw  no  conclusion,  whatever  the  Minor 
(185) 


1 86  The  Interdependence  of  Propositions. 

Premiss  may  give.  Given,  e.g.,  All  S  is  in  M,  it  may 
be  that  All  S  is  in  P,  or  that  No  S  is  in  P,  or  that 
Some  S  is  in  P,  or  that  Some  S  is  not  in  P. 


Again,  unless  the  Minor  Premiss  is  affirmative,  no 
matter  what  the  Major  Premiss  may  be,  you  can  draw 
no  conclusion.  For  if  the  Minor  Premiss  is  negative, 
all  that  you  know  is  that  All  S  or  Some  S  lies  some- 
where outside  M  ;  and  however  M  may  be  situated 
relatively  to  P,  that  knowledge  cannot  help  towards 
knowing  how  S  lies  relatively  to  P.  All  S  may  be  P, 
or  none  of  it,  or  part  of  it.  Given  all  M  is  in  P  ;  the 
All  S  (or  Some  S)  which  we  know  to  be  outside  of  M 
may  lie  anywhere  in  P  or  out  of  it. 


Similarly,  in  the  Second  Figure,  trial  and  simple 
inspection  of  all  possible  conditions  shows  that  there 
can  be  no  conclusion  unless  the  Major  Premiss  is 
universal,  and  one  of  the  premisses  negative. 

Another  and  more  common  way  of  eliminating  the 
invalid  forms,  elaborated  in  the  Middle  Ages,  is  to 
formulate  principles  applicable  irrespective  of  Figure, 


The  Demonstration  of  the  Syllogistic  Moods.      187 

and  to  rule  out  of  each  Figure  the  moods  that  do  not 
conform  to  them.  These  regulative  principles  are 
known  as  The  Canons  of  the  Syllogism. 

Canon  I.  In  every  syllogism  there  should  be  three, 
and  not  more  than  three,  terms,  and  the  terms  must 
be  used  throughout  in  the  same  sense. 

It  sometimes  happens,  owing  to  the  ambiguity  of 
words,  that  there  seem  to  be  three  terms  when  there 
are  really  four.  An  instance  of  this  is  seen  in  the 
sophism  : — 

He  who  is  most  hungry  eats  most. 
He  who  eats  least  is  most  hungry. 
/.  He  who  eats  least  eats  most. 

This  Canon,  however,  though  it  points  to  a  real  danger 
of  error  in  the  application  of  the  syllogism  to  actual 
propositions,  is  superfluous  in  the  consideration  of 
purely  formal  implication,  it  being  a  primary  assump- 
tion that  terms  are  univocal,  and  remain  constant 
through  any  process  of  inference. 

Under  this  Canon,  Mark  Duncan  says  (Inst.  Log., 
iv.  3,  2),  is  comprehended  another  commonly  expressed 
in  this  form  :  There  should  be  nothing  in  the  con- 
clusion that  was  not  in  the  premisses  :  inasmuch  as-if 
there  were  anything  in  the  conclusion  that  was  in 
neither  of  the  premisses,  there  would  be  four  terms  in 
the  syllogism. 

The  rule  that  in  every  syllogism  there  must  be 
three,  and  only  three,  propositions,  sometimes  given 
as  a  separate  Canon,  is  only  a  corollary  from  Canon  I. 

Canon  II.  The  Middle  Term  must  be  distributed 
once  at  least  in  the  Premisses. 

The  Middle  Term  must  either  be  wholly  in,  or 
wholly  out  of,  one  or  other  of  the  Extremes  before 


1 88  The  Interdependence  of  Propositions. 

it  can  be  the  means  of  establishing  a  connexion 
between  them.  If  you  know  only  that  it  is  partly  in 
both,  you  cannot  know  from  that  how  they  lie  relatively 
to  one  another  :  and  similarly  if  you  know  only  that  it 
is  partly  outside  both. 

The  Canon  of  Distributed  Middle  is  a  sort  of  counter- 
relative  supplement  to  the  Dictum  de  Omni.  Whatever 
is  predicable  of  a  whole  distributively  is  predicable  of 
all  its  several  parts.  If  in  neither  premiss  there  is  a 
predication  about  the  whole,  there  is  no  case  for  the 
application  of  the  axiom. 

Canon  III.  No  term  should  be  distributed  in  the 
conclusion  that  was  not  distributed  in  the  premisses. 

If  an  assertion  is  not  made  about  the  whole  of  a 
term  in  the  premisses,  it  cannot  be  made  about  the 
whole  of  that  term  in  the  conclusion  without  going 
beyond  what  has  been  given. 

The  breach  of  this  rule  in  the  case  of  the  Major 
term  is  technically  known  as  the  Illicit  Process  of  the 
Major :  in  the  case  of  the  Minor  term,  Illicit  Process 
of  the  Minor. 

Great  use  is  made  of  this  canon  in  cutting  off  invalid 
moods.  It  must  be  remembered  that  the  Predicate 
term  is  "distributed"  or  taken  universally  in  O  (Some 
S  is  not  in  P)  as  well  as  in  E  (No  S  is  in  P) ;  and 
that  P  is  never  distributed  in  affirmative  propositions. 

Canon  IV.  No  conclusion  can  be  drawn  from  two 
negative  premisses. 

Two  negative  premisses  are  really  tantamount  to  a 
declaration  that  there  is  no  connexion  whatever  between 
the  Major  and  the  Minor  (as  quantified  in  the  premisses) 
and  the  term  common  to  both  premisses  ;  in  short,  that 
this  is  not  a  Middle  term — that  the  condition  of  a  valid 
Syllogism  does  not  exist. 


The  Demonstration  of  the  Syllogistic  Moods.     189 

There  is  an  apparent  exception  to  this  when  the 
real  Middle  in  an  argument  is  a  contrapositive  term, 
not-M.  Thus  :— 

Nobody  who  is  not  thirsty  is  suffering  from  fever. 
This  person  is  not  thirsty. 
.'.  He  is  not  suffering  from  fever. 

But  in  such  cases  it  is  really  the  absence  of  a  quality 
or  rather  the  presence  of  an  opposite  quality  on  which 
we  reason  ;  and  the  Minor  Premiss  is  really  Affirmative 
of  the  form  S  is  in  not-M. 

Canon  V.  If  one  premiss  is  negative,  the  conclusion 
must  be  negative. 

If  one  premiss  is  negative,  one  of  the  Extremes 
must  be  excluded  in  whole  or  in  part  from  the  Middle 
term.  The  other  must  therefore  (under  Canon  IV.) 
declare  some  coincidence  between  the  Middle  term  and 
the  other  extreme ;  and  the  conclusion  can  only  affirm 
exclusion  in  whole  or  in  part  from  the  area  of  this 
coincidence. 

Canon  VI.  No  conclusion  can  be  drawn  from  two 
particular  premisses. 

This  is  evident  upon  a  comparison  of  terms  in  all 
possible  positions,  but  it  can  be  more  easily  demon- 
strated with  the  help  of  the  preceding  canons.  The 
premisses  cannot  both  be  particular  and  yield  a  con- 
clusion without  breaking  one  or  other  of  those  canons. 

Suppose  both  are  affirmative,  II,  the  Middle  is  not 
distributed  in  either  premiss. 

Suppose  one  affirmative  and  the  other  negative,  IO, 
or  OI.  Then,  whatever  the  Figure  may  be,  that  is, 
whatever  the  order  of  the  terms,  only  one  term  can  be 
distributed,  namely,  the  predicate  of  O.  This  (Canon 
II.)  must  be  the  Middle.  But  in  that  case  there  must 


1 90  The  Interdependence  of  Propositions. 

be  Illicit  Process  of  the  Major  (Canon  III.),  for  one  of 
the  premisses  being  negative,  the  conclusion  is  negative 
(Canon  V.),  and  P  its  predicate  is  distributed.  Briefly, 
in  a  negative  mood,  both  Major  and  Middle  must  be 
distributed,  and  if  both  premisses  are  particular  this 
cannot  be. 

Canon  VII.  If  one  Premiss  is  particular  the  con- 
clusion is  particular. 

This  canon  is  sometimes  combined  with  what  we 
have  given  as  Canon  V.,  in  a  single  rule :  "  The 
conclusion  follows  the  weaker  premiss  ". 

It  can  most  compendiously  be  demonstrated  with 
the  help  of  the  preceding  canons. 

Suppose  both  premisses  affirmative,  then,  if  one  is 
particular,  only  one  term  can  be  distributed  in  the 
premisses,  namely,  the  subject  of  the  Universal 
affirmative  premiss.  By  Canon  II.,  this  must  be  the 
Middle,  and  the  Minor,  being  undistributed  in  the 
Premisses,  cannot  be  distributed  in  the  conclusion. 
That  is,  the  conclusion  cannot  be  Universal — must  be 
particular. 

Suppose  one  Premiss  negative,  the  other  affirmative. 
One  premiss  being  negative,  the  conclusion  must  be 
negative,  and  P  must  be  distributed  in  the  conclusion. 
Before,  then,  the  conclusion  can  be  universal,  all  three 
terms,  S,  M,  and  P,  must,  by  Canons  II.  and  III.,  be 
distributed  in  the  premisses.  But  whatever  the  Figure 
of  the  premisses,  only  two  terms  can  be  distributed. 
For  if  one  of  the  Premisses  be  O,  the  other  must  be  A, 
and  if  one  of  them  is  E,  the  other  must  be  I.  Hence 
the  conclusion  must  be  particular,  otherwise  there  will 
be  illicit  process  of  the  Minor,  or  of  the  Major,  or  of 
the  Middle. 

The  argument  may  be  more  briefly  put  as  follows  : 


The  Demonstration  of  the  Syllogistic  Moods.     191 

In  an  affirmative  mood,  with  one  premiss  particular, 
only  one  term  can  be  distributed  in  the  premisses,  and 
this  cannot  be  the  Minor  without  leaving  the  Middle 
undistributed.  In  a  negative  mood,  with  one  premiss 
particular,  only  two  terms  can  be  distributed,  and  the 
Minor  cannot  be  one  of  them  without  leaving  either 
the  Middle  or  the  Major  undistributed. 


Armed  with  these  canons,  we  can  quickly  determine, 
given  any  combination  of  three  propositions  in  one  of 
the  Figures,  whether  it  is  or  is  not  a  valid  Syllogism. 

Observe  that  though  these  canons  hold  for  all  the 
Figures,  the  Figure  must  be  known,  in  all  combinations 
containing  A  or  O,  before  we  can  settle  a  question  of 
validity  by  Canons  II.  and  III.,  because  the  distribution 
of  terms  in  A  and  O  depends  on  their  order  in 
predication. 

Take  AEE.     In  Fig.  I.— 

All  M  is  in  P 
No  S  is  in  M 
No  S  is  in  P— 

the  conclusion  is  invalid  as  involving  an  illicit  process 
of  the  Major.     P  is  distributed  in  the  conclusion  and 
not  in  the  premisses. 
In  Fig.  II.     AEE— 

All  P  is  in  M 
No  S  is  in  M 
No  S  is  in  P— 

the  conclusion  is  valid  (Camestres). 


1 92  The  Interdependence  of  Propositions. 

In  Fig.  III.     AEE— 

All  M  is  in  P 
No  M  is  in  S 
No  S  is  in  P— 

the  conclusion  is  invalid,  there  being  illicit  process  of 
the  Major. 

In  Fig.  IV.  AEE  is  valid  (Camenes). 

Take  EIO.  A  little  reflection  shows  that  this  com- 
bination is  valid  in  all  the  Figures  if  in  any,  the  dis- 
tribution of  the  terms  in  both  cases  not  being  affected 
by  their  order  in  predication.  Both  E  and  I  are  simply 
convertible.  That  the  combination  is  valid  is  quickly 
seen  if  we  remember  that  in  negative  moods  both 
Major  and  Middle  must  be  distributed,  and  that  this  is 
done  by  E. 

EIE  is  invalid,  because  you  cannot  have  a  universal 
conclusion  with  one  premiss  particular. 

All  is  valid  in  Fig.  I.  or  Fig.  III.,  and  invalid  in 
Figs.  II.  and  IV.,  because  M  is  the  subject  of  A  in  I. 
and  III.  and  predicate  in  II.  and  IV. 

OAO  is  valid  only  in  Fig.  III.,  because  only  in  that 
Figure  would  this  combination  of  premisses  distribute 
both  M  and  P. 

Simple  exercises  of  this  kind  may  be  multiplied  till 
all  possible  combinations  are  exhausted,  and  it  is  seen 
that  only  the  recognised  moods  stand  the  test. 

If  a  more  systematic  way  of  demonstrating  the  valid 
moods  is  desired,  the  simplest  method  is  to  deduce 
from  the  Canons  special  rules  for  each  Figure.  Aristotle 
arrived  at  these  special  rules  by  simple  inspection,  but 
it  is  easier  to  deduce  them. 


The  Demonstration  of  the  Syllogistic  Moods.     193 

I.  In  the  First  Figure,  the  Major  Premiss  must  be 
Universal,  and  the  Minor  Premiss  affirmative. 

To  make  this  evident  by  the  Canons,  we  bear  in 
mind  the  Scheme  or  Figure — 

M  in  P 
S  in  M— 

and  try  the  alternatives  of  Affirmative  Moods  and 
Negative  Moods.  Obviously  in  an  affirmative  mood 
the  Middle  is  undistributed  unless  the  Major  Premiss 
is  Universal.  In  a  negative  mood,  (i)  If  the  Major 
Premiss  is  O,  the  Minor  must  be  affirmative,  and  M  is 
undistributed ;  (2)  if  the  Major  Premiss  is  I,  M  may 
be  distributed  by  a  negative  Minor  Premiss,  but  in 
that  case  there  would  be  an  illicit  process  of  the  Major 
— P  being  distributed  in  the  conclusion  (Canon  V.)  and 
not  in  the  Premisses.  Thus  the  Major  Premiss  can 
neither  be  O  nor  I,  and  must  therefore  be  either  A  or 
E,  i.e.,  must  be  Universal. 

That  the  Minor  must  be  affirmative  is  evident,  for  if 
it  were  negative,  the  conclusion  must  be  negative 
(Canon  V.)  and  the  Major  Premiss  must  be  affirmative 
(Canon  IV.),  and  this  would  involve  illicit  process  of 
the  Major,  P  being  distributed  in  the  conclusion  and 
not  in  the  Premisses. 

These  two  special  rules  leave  only  four  possible 
valid  forms  in  the  First  Figure.  There  are  sixteen 
possible  combinations  of  premisses,  each  of  the  four 
types  of  proposition  being  combinable  with  itself  and 
with  each  of  the  others. 

AA  EA  IA  OA 

AE  EE  IE  OE 

AI  El  II  OI 

AO  EO  IO  OO 


194  The  Interdependence  of  Propositions. 

Special  Rule  I.  wipes  out  the  columns  on  the  right, 
with  the  particular  major  premisses ;  and  AE,  EE, 
AO,  and  EO  are  rejected  by  Special  Rule  II.,  leaving 
BArtArA,  CElArEnt,  DArll  and  FErlO. 

II.  In   the   Second   Figure,   only   Negative   Moods 
are  possible,  and  the  Major  Premiss  must  be  universal. 

Only  Negative  moods  are  possible,  for  unless  one 
premiss  is  negative,  M  being  the  predicate  term  in 
both — 

Pin  M 

Sin  M— 

is  undistributed. 

Only  negative  moods  being  possible,  there  will  be 
illicit  process  of  the  Major  unless  the  Major  Premiss 
is  universal,  P  being  its  subject  term. 

These  special  rules  reject  AA  and  AI,  and  the  two 
columns  on  the  right. 

To  get  rid  of  EE  and  EO,  we  must  call  in  the 
general  Canon  IV. ;  which  leaves  us  with  EA,  AE, 
El,  and  AO  —  CE^ArE,  CAmEstrEs,  FEj/I»O, 

BArQJKX 

III.  In  the  Third  Figure,  the  Minor  Premiss  must 
be  affirmative. 

Otherwise,  the  conclusion  would  be  negative,  and 
the  Major  Premiss  affirmative,  and  there  would  be 
illicit  process  of  the  Major,  P  being  the  predicate  term 
in  the  Major  Premiss. 

M  in  P 
M  in  S. 

This  cuts  off  AE,  EE,  IE,  OE,  AO,  EO,  IO,  OO,— 
the  second  and  fourth  rows  in  the  above  list. 

II  and  OI  are  inadmissible  by  Canon  VI.  ;   which 


The  Demonstration  oj  the  Syllogistic  Moods.     195 

leaves  AA,  IA,  AI,  EA,  OA,  El — DArA/tfl,  DIsAmls, 
DA/Ld,  FE/A//O«,  BOMn/O,  FErLfO—  three  affir- 
mative moods  and  three  negative. 

IV.  The  Fourth  Figure  is  fenced  by  three  special 
rules,  (i)  In  negative  moods,  the  Major  Premiss  is 
universal.  (2)  If  the  Minor  is  negative,  both  premisses 
are  universal.  (3)  If  the  Major  is  affirmative,  the 
Minor  is  universal. 

(1)  Otherwise,  the  Figure  being 

Pin  M 
M  in  S, 

there  would  be  illicit  process  of  the  Major. 

(2)  The  Major  must  be  universal  by  special  rule  (i), 
and  if  the  Minor  were  not  also  universal,  the  Middle 
would  be  undistributed. 

(3)  Otherwise  M  would  be  undistributed. 

Rule  (i)  cuts  off  the  right-hand  column,  OA,  OE, 
OI,  and  OO ;  also  IE  and  IO. 

Rule  (2)  cuts  off  AO,  EO. 

Rule  (3)  cuts  off  AI,  II. 

EE  goes  by  general  Canon  IV. ;  and  we  are  left 
with  AA,  AE,  IA,  EA,  El— BMwA«/I/,  CAniEnEs, 
,  FEjA/O,  FrEslsOn. 


CHAPTER  IV. 

THE  ANALYSIS  OF  ARGUMENTS  INTO   SYLLOGISTIC 
FORMS. 

TURNING  given  arguments  into  syllogistic  form  is  apt 
to  seem  as  trivial  and  useless  as  it  is  easy  and 
mechanical.  In  most  cases  the  necessity  of  the  con- 
clusion is  as  apparent  in  the  plain  speech  form  as  in 
the  artificial  logical  form.  The  justification  of  such 
exercises  is  that  they  give  familiarity  with  the  instru- 
ment, serving  at  the  same  time  as  simple  exercises  in 
ratiocination :  what  further  uses  may  be  made  of  the 
instrument  once  it  is  mastered,  we  shall  consider  as 
we  proceed. 

I. — FIRST  FIGURE. 

Given  the  following  argument  to  be  put  into  Syllo- 
gistic form  :  "  No  war  is  long  popular  :  for  every  war 
increases  taxation ;  and  the  popularity  of  anything 
that  touches  the  pocket  is  short-lived  ". 

The  simplest  method  is  to  begin  with  the  conclusion 
— "No  war  is  long  popular" — No  S  is  P — then  to 
examine  the  argument  to  see  whether  it  yields  premisses 
of  the  necessary  form.  Keeping  the  form  in  mind, 
Celarent  of  Fig.  I. — 

No  M  is  P 
All  S  is  M 
No  S  is  P— 
(196) 


The  Analysis  of  Arguments  into  Syllogistic  Forms.    197 

we  see  at  once  that  "  Every  war  increases  taxation  "  is 
of  the  form  All  S  is  M.  Does  the  other  sentence  yield 
the  Major  Premiss  No  M  is  P,  when  M  represents  the 
increasing  of  taxation,  i.e.,  a  class  bounded  by  that 
attribute  ?  We  see  that  the  last  sentence  of  the  argu- 
ment is  equivalent  to  saying  that  "  Nothing  that 
increases  taxation  is  long  popular  "  ;  and  this  with  the 
Minor  yields  the  conclusion  in  Celarent. 

Nothing  that  increases  taxation  is  long  popular. 
Every  war  increases  taxation. 
No  war  is  long  popular. 

Observe,  now,  what  in  effect  we  have  done  in  thus 
reducing  the  argument  to  the  First  Figure.  In  effect, 
a  general  principle  being  alleged  as  justifying  a  certain 
conclusion,  we  have  put  that  principle  into  such  a  form 
that  it  has  the  same  predicate  with  the  conclusion. 
All  that  we  have  then  to  do  in  order  to  inspect  the 
validity  of  the  argument  is  to  see  whether  the  subject 
of  the  conclusion  is  contained  in  the  subject  of  the 
general  principle.  Is  war  one  of  the  things  that 
increase  taxation  ?  Is  it  one  of  that  class  ?  If  so, 
then  it  cannot  long  be  popular,  long  popularity  being 
an  attribute  that  cannot  be  affirmed  of  any  of  that 
class. 

Reducing  to  the  first  figure,  then,  amounts  simply 
to  making  the  predication  of  the  proposition  alleged 
as  ground  uniform  with  the  conclusion  based  upon  it. 
The  minor  premiss  or  applying  proposition  amounts  to 
saying  that  the  subject  of  the  conclusion  is  contained  in 
the  subject  of  the  general  principle.  Is  the  subject  of 
the  conclusion  contained  in  the  subject  of  the  general 
principle  when  the  two  have  identical  predicates  ?  If 


198  The  Interdependence  of  Propositions. 

so,  the  argument  falls  at  once  under  the   Dictum  de 
Omni  ef  Nullo. 


Two  things  may  be  noted  concerning  an  argument 
thus  simplified. 

1.  It  is  not  necessary,  in  order  to  bring  an  argument 
under  the  dictum  de  omni,  to  reduce  the  predicate  to  the 
form  of  an  extensive  term.     In  whatever  form,  abstract 
or  concrete,  the  predication  is  made  of  the  middle  term, 
it  is  applicable  in  the  same  form  to  that  which  is  con- 
tained in  the  middle  term. 

2.  The  quantity  of  the  Minor  Term  does  not  require 
special  attention,  inasmuch  as  the  argument  does  not 
turn  upon  it.     In  whatever  quantity  it  is  contained  in 
the  Middle,  in  that  quantity  is  the  predicate  of  the 
Middle  predicable  of  it. 

These  two  points  being  borne  in  mind,  the  attention 
may  be  concentrated  on  the  Middle  Term  and  its 
relations  with  the  extremes. 

That  the  predicate  may  be  left  unanalysed  without 
affecting  the  simplicity  of  the  argument  or  in  any  way 
obscuring  the  exhibition  of  its  turning-point,  has  an 
important  bearing  on  the  reduction  of  Modals.  The 
modality  may  be  treated  as  part  of  the  predicate  without 
in  any  way  obscuring  what  it  is  the  design  of  the  syllo- 
gism to  make  clear.  We  have  only  to  bear  in  mind  that 
however  the  predicate  may  be  qualified  in  the  pre- 
misses, the  same  qualification  must  be  transferred  to 
the  conclusion.  Otherwise  we  should  have  the  fallacy 
of  Four  Terms,  quaternio  terminomm. 

To  raise  the  question  :  What  is  the  proper  form  for 
a  Modal  of  Possibility,  A  or  I  ?  is  to  clear  up  in  an 
important  respect  our  conceptions  of  the  Universal 
proposition,  "  Victories  may  be  gained  by  accident  ". 


Tlie  Analysis  of  Arguments  into  Syllogistic  Forms.    199 

Should  this  be  expressed  as  A  or  I  ?  Is  the  predicate 
applicable  to  All  victories  or  only  to  Some  ?  Obviously 
the  meaning  is  that  of  any  victory  it  may  be  true  that 
it  was  gained  by  accident,  and  if  we  treat  the  "  mode  " 
as  part  of  the  predicate  term  "  things  that  may  be 
gained  by  accident,"  the  form  of  the  proposition  is  All 
S  is  in  P. 

But,  it  may  be  asked,  does  not  the  proposition  that 
victories  may  be  gained  by  accident  rest,  as  a  matter 
of  fact,  on  the  belief  that  some  victories  have  been 
gained  in  this  way  ?  And  is  not,  therefore,  the  proper 
form  of  proposition  Some  S  is  P  ? 

This,  however,  is  a  misunderstanding.  What  we 
are  concerned  with  is  the  formal  analysis  of  proposi- 
tions as  given.  And  Some  victories  have  been  gained 
by  accident  is  not  the  formal  analysis  of  Victories  may 
be  gained  by  accident.  The  two  propositions  do  not 
give  the  same  meaning  in  different  forms  :  the  meaning 
as  well  as  the  form  is  different.  The  one  is  a  statement 
of  a  matter  of  fact :  the  other  of  an  inference  founded 
on  it.  The  full  significance  of  the  Modal  proper  may 
be  stated  thus  :  In  view  of  the  fact  that  some  victories 
have  been  gained  by  accident,  we  are  entitled  to  say  ot 
any  victory,  in  the  absence  of  certain  knowledge,  that 
it  may  be  one  of  them. 

A  general  proposition,  in  short,  is  a  proposition 
about  a  genus,  taken  universally. 

II. — SECOND  FIGURE. 

For  testing  arguments  from  general  principles,  the 
First  Figure  is  the  simplest  and  best  form  of  analysis. 

But  there  is  one  common  class  of  arguments  that 
fall  naturally,  as  ordinarily  expressed,  into  the  Second 


2oo  The  Interdependence  of  Propositions. 

Figure,  namely,  negative  conclusions  from  the  absence 
of  distinctive  signs  or  symptoms,  or  necessary  con- 
ditions. 

Thirst,  for  example,  is  one  of  the  symptoms  of  fever : 
if  a  patient  is  not  thirsty,  you  can  conclude  at  once 
that  his  illness  is  not  fever,  and  the  argument,  fully 
expressed,  is  in  the  Second  Figure. 

All  fever-stricken  patients  are  thirsty. 
This  patient  is  not  thirsty. 
.*.  He  is  not  fever-stricken. 

Arguments  of  this  type  are  extremely  common. 
Armed  with  the  general  principle  that  ill-doers  are  ill- 
dreaders,  we  argue  from  a  man's  being  unsuspicious 
that  he  is  not  guilty.  The  negative  diagnosis  of  the 
physician,  as  when  he  argues  from  the  absence  of  sore 
throat  or  the  absence  of  a  white  speck  in  the  throat 
that  the  case  before  him  is  not  one  of  scarlatina  or 
diphtheria,  follows  this  type :  and  from  its  utility  in 
making  such  arguments  explicit,  the  Second  Figure 
may  be  called  the  Figure  of  Negative  Diagnosis. 

It  is  to  be  observed,  however,  that  the  character  of 
the  argument  is  best  disclosed  when  the  Major  Premiss 
is  expressed  by  its  Converse  by  Contraposition.  It 
is  really  from  the  absence  of  a  symptom  that  the 
physician  concludes ;  as,  for  example :  "  No  patient 
that  has  not  a  sore  throat  is  suffering  from  scarlatina". 
And  the  argument  thus  expressed  is  in  the  First 
Figure.  Thus  the  reduction  of  Baroko  to  the  First 
Figure  by  contraposition  of  the  Middle  is  vindicated  as 
a  really  useful  process.  The  real  Middle  is  a  contra- 
positive  term,  and  the  form  corresponds  more  closely 
to  the  reasoning  when  the  argument  is  put  in  the  First 
Figure. 


The  Analysis  of  Arguments  into  Syllogistic  Forms.    201 

The  truth  is  that  if  the  positive  term  or  sign  or 
necessary  condition  is  prominent  as  the  basis  of  the 
argument,  there  is  considerable  risk  of  fallacy.  Sore 
throat  being  one  of  the  symptoms  of  scarlatina,  the 
physician  is  apt  on  finding  this  symptom  present  to 
jump  to  a  positive  conclusion.  This  is  equivalent 
technically  to  drawing  a  positive  conclusion  from 
premisses  of  the  Second  Figure. 

All  scarlatina  patients  have  sore  throat. 
This  patient  has  sore  throat. 

A  positive  conclusion  here  is  technically  known  as  a 
Non-Sequitur  (Doesn't  follow).  So  with  arguments 
from  the  presence  of  a  necessary  condition  which  is 
only  one  of  many.  Given  that  it  is  impossible  to  pass 
without  working  at  the  subject,  or  that  it  is  impossible 
to  be  a  good  marksman  without  having  a  steady  hand, 
we  are  apt  to  argue  that  given  also  the  presence  of  this 
condition,  a  conclusion  is  implicated.  But  really  the 
premisses  given  are  only  two  affirmatives  of  the 
Second  Figure. 

"  It  is  impossible  to  pass  without  working  at  the  sub- 
ect." 

This,  put  into  the  form  No  not-M  is  P,  is  to  say  that 
"None  who  have  not  worked  can  pass".  This  is 
equivalent,  as  the  converse  by  contraposition,  with — 

All  capable  of  passing  have  worked  at  the  subject. 

But  though  Q  has  worked  at  the  subject,  it  does  not 
follow  that  he  is  capable  of  passing.  Technically  the 
middle  is  undistributed.  On  the  other  hand,  if  he  has 
not  worked  at  the  subject,  it  follows  that  he  is  not 
capable  of  passing.  We  can  draw  a  conclusion  at 


202  The  Interdependence  of  Propositions. 

once   from   the   absence    of  the    necessary   condition, 
though  none  can  be  drawn  from  its  presence  alone. 

THIRD  FIGURE. 

Arguments  are  sometimes  advanced  in  the  form 
of  the  Third  Figure.  For  instance  :  Killing  is  not 
always  murder :  for  tyrannicide  is  not  murder,  and 
yet  it  is  undoubtedly  killing.  Or  again  :  Unpleasant 
things  are  sometimes  salutary :  for  afflictions  are 
sometimes  so,  and  no  affliction  can  be  called  pleasant. 

These  arguments,  when  analysed  into  terms,  are, 
respectively,  Felapton  and  Disamis. 

No  tyrannicide  is  murder; 
All  tyrannicide  is  killing  ; 
Some  killing  is  not  murder. 

Some  afflictions  are  salutary  things ; 
All  afflictions  are  unpleasant  things  ; 
Some  unpleasant  things  are  salutary  things. 

The  syllogistic  form  cannot  in  such  cases  pretend  to 
be  a  simplification  of  the  argument.  The  argument 
would  be  equally  unmistakable  if  advanced  in  this 
form:  Some  S  is  not  P,  for  example,  M.  Some 
killing  is  not  murder,  e.g.,  tyrannicide.  Some  un- 
pleasant things  are  salutary,  e.g.,  some  afflictions. 

There  is  really  no  "deduction"  in  the  third  figure, 
no  leading  down  from  general  to  particular.  The 
middle  term  is  only  an  example  of  the  minor.  It  is 
the  syllogism  of  Contradictory  Examples. 

In  actual  debate  examples  are  produced  to  disprove 
a  universal  assertion,  affirmative  or  negative.  Suppose 
it  is  maintained  that  every  wise  man  has  a  keen  sense 
of  humour.  You  doubt  this :  you  produce  an  instance 
of  the  opposite,  say  Milton.  The  force  of  your  contra- 
dictory instance  is  not  increased  by  exhibiting  the 


The  Analysis  of  Arguments  into  Syllogistic  Forms.    203 

argument  in  syllogistic  form  :  the  point  is  not  made 
clearer. 

The  Third  Figure  was  perhaps  of  some  use  in  Yes 
and  No  Dialectic.  When  you  had  to  get  everything 
essential  to  your  conclusion  definitely  admitted,  it  was 
useful  to  know  that  the  production  of  an  example  to 
refute  a  generality  involved  the  admission  of  two 
propositions.  You  must  extract  from  your  opponent 
both  that  Milton  was  a  wise  man,  and  that  Milton  had 
not  a  keen  sense  of  humour,  before  you  could  drive 
him  from  the  position  that  all  wise  men  possess  that 
quality. 

Examples  for  Analysis. 

Scarlet  flowers  have  no  fragrance:  this  flower  has  no 
fragrance :  does  it  follow  that  this  flower  is  of  a  scarlet 
colour  ? 

Interest  in  the  subject  is  an  indispensable  condition  of 
learning  easily:  Z  is  interested  in  the  subject:  he  is  bound,, 
therefore,  to  learn  easily. 

It  is  impossible  to  be  a  good  shot  without  having  a  steady 
hand :  John  has  a  steady  hand  :  he  is  capable,  therefore,  of 
becoming  a  good  shot. 

Some  victories  have  been  won  by  accident ;  for  example, 
Maiwand. 

Intemperance  is  more  disgraceful  than  cowardice,  be- 
cause people  have  more  opportunities  of  acquiring  control 
of  their  bodily  appetites. 

"  Some  men  are  not  fools,  yet  all  men  are  fallible." 
What  follows  ? 

"  Some  men  allow  that  their  memory  is  not  good  :  every 
man  believes  in  his  own  judgment."  What  is  the  con- 
clusion, and  in  what  Figure  and  Mood  may  the  argument 
be  expressed  ? 

"An  honest  man's  the  noblest  work  of  God:  Z  is  an 
honest  man  "  :  therefore,  he  is — what  ? 

Examine   the  logical   connexion    between  the  following 


204  The  Interdependence  of  Propositions. 

"exclamation"  and  "answer":  "But  I  hear  some  one 
exclaiming  that  wickedness  is  not  easily  concealed.  To 
which  I  answer,  Nothing  great  is  easy." 

"  If  the  attention  is  actively  aroused,  sleep  becomes 
impossible :  hence  the  sleeplessness  of  anxiety,  for  anxiety 
is  a  strained  attention  upon  an  impending  disaster." 

"  To  follow  truth  can  never  be  a  subject  of  regret ;  free 
inquiry  does  lead  a  man  to  regret  the  days  of  his  childish 
faith ;  therefore  it  is  not  following  truth." — J.  H.  Newman. 

He  would  not  take  the  crown :  Therefore  'tis  certain  he 
was  not  ambitious. 

As  he  was  valiant,  I  honour  him  ;  as  he  was  ambitious,  I 
slew  him. 

The  Utopians  learned  the  language  of  the  Greeks  with 
more  readiness  because  they  were  originally  of  the  same 
race  with  them. 

Nothing  which  is  cruel  can  be  expedient,  for  cruelty  is 
most  revolting  to  the  nature  of  man. 

"The  fifth  century  saw  the  foundation  of  the  Frank 
dominion  in  Gaul,  and  the  first  establishment  ot  the  German 
races  in  Britain.  The  former  was  effected  in  a  single  long 
reign,  by  the  energy  of  one  great  ruling  tribe,  which  had 
already  modified  its  traditional  usages,  and  now,  by  the 
adoption  of  the  language  and  religion  of  the  conquered, 
prepared  the  way  for  a  permanent  amalgamation  with 
them."  In  the  second  of  the  above  sentences  a  general 
proposition  is  assumed.  Show  in  syllogistic  form  how  the 
last  proposition  in  the  sentence  depends  upon  it. 

"  I  do  not  mean  to  contend  that  active  benevolence  may 
not  hinder  a  man's  advancement  in  the  world :  for  advance- 
ment greatly  depends  upon  a  reputation  for  excellence  in 
some  one  thing  of  which  the  world  perceives  that  it  has 
present  need  :  and  an  obvious  attention  to  other  things, 
though  perhaps  not  incompatible  with  the  excellence  itself, 
may  easily  prevent  a  person  from  obtaining  a  reputation  for 
it."  Pick  out  the  propositions  here  given  as  interdependent. 
Examine  whether  the  principle  alleged  is  sufficiently  general 
to  necessitate  a  conclusion.  In  what  iorm  would  it  be  so  ? 


CHAPTER  V. 
ENTHYMEMES. 

THERE  is  a  certain  variety  in  the  use  of  the  word 
Enthymeme  among  logicians.  In  the  narrowest 
sense,  it  is  a  valid  formal  syllogism,  with  one  premiss 
suppressed.  In  the  widest  sense  it  is  simply  an  argu- 
ment, valid  or  invalid,  formal  in  expression  or  informal, 
with  only  one  premiss  put  forward  or  hinted  at,  the 
other  being  held  in  the  mind  (cv  tfv/Aw).  This  last  is 
the  Aristotelian  sense. 

It  is  only  among  formal  logicians  of  the  straitest 
sect  that  the  narrowest  sense  prevails.  Hamilton 
divides  Enthymemes  into  three  classes  according  as  it 
is  the  Major  Premiss,  the  Minor  Premiss,  or  the  Con- 
clusion that  is  suppressed.  Thus,  a  full  syllogism 
being  : — 

All  liars  are  cowards : 
Caius  is  a  liar  : 
.*.  Caius  is  a  coward  : — 

this  may  be  enthymematically  expressed  in  three  ways. 

I.  Enthymeme   of  the   First    Order   (Major  under- 
stood}. 

Caius  is  a  coward  ;  for  Caius  is  a  liar. 

II.  Enthymeme  of  the  Second  Order  (Minor  under- 
stood]. 

Caius  is  a  coward  ;  for  all  liars  are  cowards. 
(205) 


206  The  Interdependence  of  Propositions. 

III.  Enthymeme  of  the  Third  Order  {Conclusion 
understood}. 

All  liars  are  cowards,  and  Caius  is  a  liar. 

The  Third  Order  is  a  contribution  of  Hamilton's 
own.  It  is  superfluous,  inasmuch  as  the  conclusion  is 
never  suppressed  except  as  a  rhetorical  figure  of  speech. 
Hamilton  confines  the  word  Enthymeme  to  valid  argu- 
ments, in  pursuance  of  his  view  that  Pure  Logic  has 
no  concern  with  invalid  arguments. 

Aristotle  used  Enthymeme  in  the  wider  sense  of  an 
elliptically  expressed  argument.  There  has  been  some 
doubt  as  to  the  meaning  of  his  definition,  but  that 
disappears  on  consideration  of  his  examples.  He 
defines  an  Enthymeme  (Prior  Analyt.,  ii.  27)  as  "  a 
syllogism  from  probabilities  or  signs  "  (crvAAoyioyxos  e£ 
€tKOT(uv  17  cny/mW).  The  word  syllogism  in  this  con- 
nexion is  a  little  puzzling.  But  it  is  plain  from  the 
examples  he  gives  that  he  meant  here  by  syllogism  not 
even  a  correct  reasoning,  much  less  a  reasoning  in  the 
explicit  form  of  three  terms  and  three  propositions.  He 
used  syllogism,  in  fact,  in  the  same  loose  sense  in  which 
we  use  the  words  reasoning  and  argument,  applying 
without  distinction  of  good  and  bad. 

The  sign,  he  says,  is  taken  in  three  ways,  in  as 
many  ways  as  there  are  Syllogistic  Figures. 

(1)  A  sign  interpreted  in  the  First  Figure  is  conclu- 
sive.    Thus  :   "  This  person  has  been  drowned,  for  he 
has  froth  in  the  trachea"      Taken  in  the  First  Figure 
with  "All  who  have  froth  in  the  trachea  have  been 
drowned  "  as  major  premiss,  this  argument  is  valid. 
The  sign  is  conclusive. 

(2)  "  This  patient  is  fever-stricken,  for  he*  is  thirsty." 
Assumed  that  '-All  fever-stricken  patients  are  thirsty," 


Enthymemes.  207 

this  is  an  argument  in  the  Second  Figure,  but  it  is  not 
a  valid  argument.  Thirst  is  a  sign  or  symptom  of 
fever,  but  not  a  conclusive  sign,  because  it  is  indicative 
of  other  ailments  also.  Yet  the  argument  has  a  certain 
probability. 

(3)  "  Wise  men  are  earnest  (O-TTOV&UOI),  for  Pittacus 
is  earnest."  Here  the  suppressed  premiss  is  that 
"  Pittacus  is  wise  ".  Fully  expressed,  the  argument  is 
in  the  Third  Figure : — 

Pittacus  is  earnest. 
Pittacus  is  wise. 
.•.Wise  men  are  earnest. 

Here  again  the  argument  is  inconclusive  and  yet  it 
has  a  certain  probability.  The  coincidence  of  wisdom 
with  earnestness  in  one  notable  example  lends  a 
certain  air  of  probability  to  the  general  statement. 

Such  are  Aristotle's  examples  or  strict  parallels  to 
them.  The  examples  illustrate  also  what  he  says  in 
his  Rhetoric  as  to  the  advantages  of  enthymemes.  For 
purposes  of  persuasion  enthymemes  are  better  than 
explicit  syllogisms,  because  any  inconclusiveness  there 
may  be  in  the  argument  is  more  likely  to  pass  un- 
detected. As  we  shall  see,  one  main  use  of  the 
Syllogism  is  to  force  tacit  assumptions  into  light  and 
so  make  their  true  connexion  or  want  of  connexion 
apparent.  In  Logic  enthymemes  are  recognised  only 
to  be  shown  up  :  the  elliptical  expression  is  a  cover  for 
fallacy,  which  it  is  the  business  of  the  logician  to  strip 
off. 

In  Aristotle's  examples  one  of  the  premisses  is 
expressed.  But  often  the  arguments  of  common 
speech  are  even  less  explicit  than  this.  A  general 
principle  is  vaguely  hinted  at :  a  subject  is  referred  to 


208  The  Interdependence  of  Propositions. 

a  class  the  attributes  of  which  are  assumed  to  be 
definitely  known.  Thus  : — 

He  was  too  ambitious  to  be  scrupulous  in  his  choice  of 

means. 
He  was  too  impulsive  not  to  have  made  many  blunders. 

Each  of  these  sentences  contains  a  conclusion  and  an 
enthymematic  argument  in  support  of  it.  The  hearer 
is  understood  to  have  in  his  mind  a  definite  idea  of  the 
degree  of  ambition  at  which  a  man  ceases  to  be 
scrupulous,  or  the  degree  of  impulsiveness  that  is 
incompatible  with  accuracy. 

One  form  of  enthymeme  is  so  common  in  modern 
rhetoric  as  to  deserve  a  distinctive  name.  It  may  be 
called  the  Enthymeme  of  the  Abstractly  Denominated 
Principle.  A  conclusion  is  declared  to  be  at  variance 
with  the  principles  of  Political  Economy,  or  contrary 
to  the  doctrine  of  Evolution,  or  inconsistent  with 
Heredity,  or  a  violation  of  the  sacred  principle  of 
Freedom  of  Contract.  It  is  assumed  that  the  hearer  is 
familiar  with  the  principles  referred  to.  As  a  safe- 
guard against  fallacy,  it  may  be  well  to  make  the 
principle  explicit  in  a  proposition  uniform  with  the 
conclusion. 


CHAPTER  VI. 
THE  UTILITY  OF  THE  SYLLOGISM. 

THE  main  use  of  the  Syllogism  is  in  dealing  with 
incompletely  expressed  or  elliptical  arguments  from 
general  principles.  This  may  be  called  Enthymematic 
argument,  understanding  by  Enthymeme  an  argument 
with  only  one  premiss  put  forward  or  hinted  at,  the 
other  being  held  in  the  mind.  In  order  to  test  whether 
such  reasoning  is  sound  or  unsound,  it  is  of  advantage 
to  make  the  argument  explicit  in  Syllogistic  form. 

There  have  been  heaps  and  mazes  of  discussion 
about  the  use  of  the  Syllogism,  much  of  it  being 
profitable  as  a  warning  against  the  neglect  of  Formal 
Logic.  Again  and  again  it  has  been  demonstrated 
that  the  Syllogism  is  useless  for  certain  purposes,  and 
from  this  it  has  been  concluded  that  the  Syllogism  is 
of  no  use  at  all. 

The  inventor  of  the  Syllogism  had  a  definite 
practical  purpose,  to  get  at  the  simplest,  most  con- 
vincing, undeniable  and  irresistible  way  of  putting 
admitted  or  self-evident  propositions  so  that  their 
implication  should  be  apparent.  His  ambition  was  to 
furnish  a  method  for  the  Yes  and  No  Dialectician,  and 
the  expounder  of  science  from  self-evident  principles. 
A  question  being  put  up  for  discussion,  it  was  an 
advantage  to  analyse  it,  and  formulate  the  necessary 
H  (209) 


2io  2'he  Interdependence  of  Propositions. 

premisses  :  you  could  then  better  direct  your  interroga- 
tions or  guard  your  answers.  The  analysis  is  similarly 
useful  when  you  want  to  construct  an  argument  from 
self-evident  principles. 

All  that  the  Syllogism  could  show  was  the  consis- 
tency of  the  premisses  with  the  conclusion.  The 
conclusion  could  not  go  beyond  the  premisses,  because 
the  questioner  could  not  go  beyond  the  admissions  of 
the  respondent.  There  is  indeed  an  advance,  but  not 
an  advance  upon  the  two  premisses  taken  together. 
There  is  an  advance  upon  any  one  of  them,  and  this 
advance  is  made  with  the  help  of  the  other.  Both 
must  be  admitted  :  a  respondent  may  admit  one  with- 
out being  committed  to  the  conclusion.  Let  him 
admit  both  and  he  cannot  without  self-contradiction 
deny  the  conclusion.  That  is  all. 

Dialectic  of  the  Yes  and  No  kind  is  no  longer 
practised.  Does  any  analogous  use  for  the  Syllogism 
remain  ?  Is  there  a  place  for  it  as  a  safeguard  against 
error  in  modern  debate  ?  As  a  matter  of  fact  it  is 
probably  more  useful  now  than  it"  was  for  its  original 
purpose,  inasmuch  as  modern  discussion,  aiming  at 
literary  grace  and  spurning  exact  formality  as  smacking 
of  scholasticism  and  pedantry,  is  much  more  flabby  and 
confused.  In  the  old  dialectic  play  there  was  generally 
a  clear  question  proposed.  The  interrogative  form 
forced  this  much  on  the  disputants.  The  modern 
debater  of  the  unpedantic,  unscholastic  school  is  not 
so  fettered,  and  may  often  be  seen  galloping  wildly 
about  without  any  game  in  sight  or  scent,  his  maxim 
being  to — 

Spur  boldly  on,  and  dash  through  thick  and  thin, 
Through  sense  and  nonsense,  never  out  nor  in. 


The  Utility  of  the  Syllogism.  2 1 1 

Now  the  syllogistic  analysis  may  often  be  of  some 
use  in  helping  us  to  keep  a  clear  head  in  the  face  of  a 
confused  argument.  There  is  a  brilliant  defence  of 
the  syllogism  as  an  analysis  of  arguments  in  the  West- 
minster Review  for  January,  1828.  The  article  was  a 
notice  of  Whately's  Logic  :  it  was  written  by  J.  S. 
Mill.  For  some  reason  it  has  never  been  reprinted, 
but  it  puts  the  utility  of  the  Syllogism  on  clearer 
ground  than  Mill  afterwards  sought  for  it. 

Can  a  fallacy  in  argument  be  detected  at  once  ? 
Is  common-sense  sufficient  ?  Common-sense  would 
require  some  inspection.  How  would  it  proceed  ? 
Does  common-sense  inspect  the  argument  in  a  lump 
or  piecemeal  ?  All  at  once  or  step  by  step  ?  It 
analyses.  How  ?  First,  it  separates  out  the  proposi- 
tions which  contribute  to  the  conclusion  from  those 
which  do  not,  the  essential  from  the  irrelevant.  Then 
it  states  explicitly  all  that  may  have  been  assumed 
tacitly.  Finally,  it  enumerates  the  propositions  in 
order. 

Some  such  procedure  as  this  would  be  adopted  by 
common-sense  in  analysing  an  argument.  But  when 
common-sense  has  done  this,  it  has  exhibited  the 
argument  in  a  series  of  syllogisms. 

Such  is  Mill's  early  defence  of  the  Syllogism.  It  is 
weak  only  in  one  point,  in  failing  to  represent  how 
common-sense  would  arrive  at  the  peculiar  syllogistic 
form.  It  is  the  peculiar  form  of  logical  analysis  that 
is  the  distinction  of  the  syllogism.  When  you  have 
disentangled  the  relevant  propositions  you  have  not 
necessarily  put  them  in  this  form.  The  arguments 
given  in  text-books  to  be  cast  into  syllogistic  form, 
consist  only  as  a  rule  of  relevant  propositions,  but  they 
are  not  yet  formal  syllogisms.  But  common-sense 


212  The  Interdependence  of  Propositions. 

had  only  one  other  step  to  make  to  reach  the  distinc- 
tive form.  It  had  only  to  ask  after  analysing  the 
argument,  Is  there  any  form  of  statement  specially 
suitable  for  exhibiting  the  connexion  between  a  con- 
clusion and  the  general  principle  on  which  it  is  alleged 
to  depend  ?  Ask  yourself  the  question,  and  you  will 
soon  see  that  there  would  be  an  obvious  advantage  in 
making  the  conclusion  and  the  general  principle 
uniform,  in  stating  them  with  the  same  predicate. 
But  when  you  do  this,  as  I  have  already  shown  (p.  197) 
you  state  the  argument  in  the  First  Figure  of  the 
Syllogism. 

It  must,  however,  be  admitted  that  it  is  chiefly  for 
exhibiting,  or  forcing  into  light,  tacit  or  lurking 
assumptions  that  the  Syllogistic  form  is  of  use. 
Unless  identity  of  meaning  is  disguised  or  distorted  by 
puzzling  difference  of  language,  there  is  no  special 
illuminative  virtue  in  the  Syllogism.  The  argument 
in  a  Euclidean  demonstration  would  not  be  made 
clearer  by  being  cast  into  formal  Syllogisms. 

Again,  when  the  subject  matter  is  simple,  the 
Syllogistic  form  is  not  really  required  for  protection 
against  error.  In  such  enthymemes  as  the  following 
for  example : — 

She  must  be  clever :  she  is  so  uncompromisingly  ugly. 
Romeo  must  be  in  love  :  for  is  he  not  seventeen  ? 

it  is  plain  to  the  average  intelligence  without  any 
knowledge  of  Syllogism  that  the  argument  takes  for 
granted  a  general  proposition  and  what  the  general 
proposition  is. 

Another  thing  is  plain  to  the  average  intelligence, 
perhaps  plainer  than  to  a  proficient  in  the  use  of  the 


The  Utility  of  the  Syllogism.  213 

Syllogism.  Clearly  we  cannot  infer  with  certainty 
that  a  woman  is  clever  because  she  is  ugly,  unless  it 
is  the  case  that  all  ugly  women  are  clever.  But  a 
Syllogiser,  seeing  that  no  certain  conclusion  can  be 
drawn  except  upon  this  condition,  is  apt  to  dismiss 
the  argument  as  altogether  worthless.  This  may  be 
specified  as  an  error  incident  to  the  practice  of  the 
Syllogism,  that  it  inclines  us  to  look  for  necessarily 
conclusive  premisses,  and  to  deny  all  weight  to  any- 
thing short  of  this.  Now  in  ordinary  life  it  is  com- 
paratively seldom  that  such  premisses  can  be  found. 
We  are  obliged  to  proceed  on  maxims  that  are  not  of 
universal  scope,  and  which  lend  only  a  more  or  less 
strong  colour  of  probability  to  cases  that  can  be  brought 
under  them.  "  A  little  learning  is  a  dangerous  thing ;  " 
"  Haste  makes  waste  ; "  "  Slowness  of  speech  is  a  sign 
of  depth  of  thought ;  "  "  Vivacity  is  a  sign  of  shallow- 
ness  : "  such  are  the  "  endoxes  "  or  commonplaces  of 
popular  knowledge  that  men  bring  to  bear  in  daily  life. 
They  are  not  true  for  all  cases,  but  some  of  them  are  true 
for  most  or  for  a  good  many,  and  they  may  be  applied 
with  a  certain  probability  though  they  are  not  rigidly 
conclusive.  The  plain  man's  danger  is  that  he  apply 
them  unthinkingly  as  universals  :  the  formal  logician's 
danger  is  that,  seeing  them  to  be  inapplicable  as  uni- 
versals, he  dismisses  them  as  being  void  of  all 
argumentative  force. 

It  helps  to  fix  the  limits  of  Formal  Logic  to  remember 
that  it  lies  outside  its  bounds  to  determine  the  degree 
of  probability  attaching  to  the  application  of  approxi- 
mate truths,  such  as  are  the  staple  of  arguments  in 
ordinary  affairs.  Formal  Logic,  we  may  repeat,  is 
not  concerned  with  degrees  of  truth  or  falsehood, 
probability  or  improbability.  It  merely  shows  the 


214  The  Interdependence  of  Propositions. 

interdependency  of  certain  arguments,  the  consistency 
of  conclusion  with  premisses. 

This,  however,  is  a  function  that  might  easily  bi 
underrated.  Its  value  is  more  indirect  than  direct.  In 
showing  what  is  required  for  a  certain  conclusion,  it 
puts  us  on  the  road  to  a  more  exact  estimate  of  the 
premisses  alleged,  a  sounder  judgment  of  their 
worth.  Well  begun  is  half  done :  in  undertaking  the 
examination  of  any  argument  from  authority,  a 
formal  syllogism  is  a  good  beginning. 


CHAPTER  VII. 

CONDITIONAL  ARGUMENTS.—  HYPOTHETICAL  SYLLO- 
GISM, DISJUNCTIVE  SYLLOGISM,  AND  DILEMMA. 

THE  justification  of  including  these  forms  of  argu- 
ment in  Logic  is  simply  that  they  are  sometimes  used 
in  debate,  and  that  confusion  may  arise  unless  the 
precise  meaning  of  the  premisses  employed  is  under- 
stood. Aristotle  did  not  include  them  as  now  given  in 
his  exposition  of  the  Syllogism,  probably  because  they 
have  no  connexion  with  the  mode  of  reasoning  together 
to  which  he  appropriated  the  title.  The  fallacies  con- 
nected with  them  are  of  such  a  simple  kind  that  to 
discuss  as  a  question  of  method  the  precise  place  they 
should  occupy  in  a  logical  treatise  is  a  waste  of 
ingenuity.1 

I.  —  HYPOTHETICAL  SYLLOGISMS. 


lfAisB,Cism  MODUS 
c  !s  »°|  ?        TOLLENS 

.*.  A  is  not  B 


1  For   the  history  of    Hypothetical    Syllogism    see    Mansel's 
Aldrich,  Appendix  I. 


216  The  Interdependence  of  Propositions. 

A  so-called  Hypothetical  Syllogism  is  thus  seen  to 
be  a  Syllogism  in  which  the  major  premiss  is  a 
Hypothetical  Proposition,  that  is  to  say,  a  complex 
proposition  in  which  two  propositions  are  given  as  so 
related  that  the  truth  of  one  follows  necessarily  from 
the  truth  of  the  other. 

Two  propositions  so  related  are  technically  called 
the  Antecedent  or  Reason,  and  the  Consequent. 

The  meaning  and  implication  of  the  form,  If  A  is  B, 
C  is  D,  is  expressed  in  what  is  known  as.  the  Law  of 
Reason  and  Consequent  :— 

"  When  two  propositions  are  related  as  Reason  and 
Consequent,  the  truth  of  the  Consequent  follows  from  the 
truth  of  the  Antecedent,  and  the  falsehood  of  the  Antecedent, 
from  the  falsehood  of  the  Consequent". 

If  A  is  B,  C  is  D,  implies  that  If  C  is  not  D,  A  is 
not  B.  If  this  subject  is  educative,  it  quickens  the 
wits ;  if  it  does  not  quicken  the  wits,  it  is  not  educa- 
tive. 

Admitted,  then,  that  the  law  of  Reason  and  Conse- 
quent holds  between  two  propositions — that  If  A  is  B, 
C  is  D :  admitted  also  the  Antecedent,  the  truth  of 
the  Consequent  follows.  This  is  the  Modus  Ponens 
or  Positive  Mode,  where  you  reach  a  conclusion  by 
obtaining  the  admission  of  the  Antecedent.  Admit  the 
Antecedent  and  the  truth  of  the  Consequent  follows. 

With  the  same  Major  Premiss,  you  may  also,  under 
the  Law  of  Reason  and  Consequent  reach  a  conclusion 
by  obtaining  the  denial  of  the  Consequent.  This  is 
the  Modus  Tollens  or  Negative  Mode.  Deny  the  Con- 
sequent and  one  is  bound  to  deny  the  Antecedent. 

But  to  guard  against  the  fallacy  technically  known 
as  Fallacia  Consequentis,  we  must  observe  what  the 
relation  of  Reason  and  Consequent  does  not  imply. 


Conditional  Arguments.  217 

The  truth  of  the  Consequent  does  not  involve  the 
truth  of  the  Antecedent,  and  the  falsehood  of  the  Ante- 
cedent does  not  involve  the  falsehood  of  the  Conse- 
quent. 

"  If  the  harbour  is  frozen,  the  ships  cannot  come 
in."  If  the  harbour  is  not  frozen,  it  does  not  follow 
that  the  ships  can  come  in  :  they  may  be  excluded  by 
other  causes.  And  so,  though  they  cannot  come  in,  it 
does  not  follow  that  the  harbour  is  frozen. 
Questions  Connected  with  Hypothetical  Syllogisms. 

(1)  Are   they  properly   called    Syllogisms?      This   is 
purely  a  question  of  Method  and  Definition.     If  we 
want  a  separate  technical  name  for  forms  of  argument 
in  which  two  terms  are  reasoned  together  by  means  of 
a  third,  the  Hypothetical  Syllogism,  not  being  in  such 
a  form,  is  not  properly  so  called.     The  iact  is  that  for 
the  purposes  of  the  Hypothetical  Argument,  we  do  not 
require  an  analysis  into  terms  at  all :  it  is  superfluous  : 
we  are  concerned  only  with  the  affirmation  or  denial  of 
the  constituent  propositions  as  wholes. 

But  if  we  extend  the  word  Syllogism  to  cover  all 
arguments  in  which  two  propositions  necessarily 
involve  a  third,  the  Hypothetical  Argument  is  on  this 
understanding  properly  enough  called  a  Syllogism. 

(2)  Is    the   inference    in    the    Hypothetical    Syllogism 
Mediate  or  Immediate  ? 

To  answer  this  question  we  have  to  consider  whether 
the  Conclusion  can  be  drawn  from  either  of  the  two 
premisses  without  the  help  of  the  other.  If  it  is 
possible  immediately,  it  must  be  educible  directly 
either  from  the  Major  Premiss  or  from  the  Minor. 

(a)  Some  logicians  argue  as  if  the  Conclusion  were 
immediately  possible  from  the  Major  Premiss.  The 
Minor  Premiss  and  the  Conclusion,  they  urge,  are 


2i8  The  Interdependence  oj  Propositions. 

simply  equivalent  to  the  Major  Premiss.  But  this  is 
a  misunderstanding.  "  If  A  is  B,  C  is  D,"  is  not 
equivalent  to  "  A  is  B,  therefore  C  is  D  ".  "  If  the 
harbour  is  frozen,  the  ships  cannot  come  in  "  is  not  to 
say  that  "  the  harbour  is  frozen,  and  therefore,"  etc. 
The  Major  Premiss  merely  affirms  the  existence  of  the 
relation  of  Reason  and  Consequent  between  the  two 
propositions.  But  we  cannot  thereupon  assert  the 
Conclusion  unless  the  Minor  Premiss  is  also  conceded  : 
that  is,  the  inference  of  the  Conclusion  is  Mediate, 
as  being  from  two  premisses  and  not  from  one 
alone. 

(b}  Similarly  with  Hamilton's  contention  that  the 
Conclusion  is  inferrible  immediately  from  the  Minor 
Premiss,  inasmuch  as  the  Consequent  is  involved  in 
the  Reason.  True,  the  Consequent  is  involved  in  the 
Reason  :  but  we  cannot  infer  from  "  A  is  B  "  to  "  C  is 
D,"  unless  it  is  conceded  that  the  relation  of  Reason 
and  Consequent  holds  between  them ;  that  is,  unless 
the  Major  Premiss  is  conceded  as  well  as  the  Minor. 

(3)  Can  Hypothetical  Syllogisms  be  rediiced  to  the 
Categorical  Form  ? 

To  oppose  Hypothetical  Syllogisms  to  Categorical 
is  misleading,  unless  we  take  note  of  the  precise 
difference  between  them.  It  is  only  in  the  form  of  the 
Major  Premiss  that  they  differ:  Minor  Premiss  and 
Conclusion  are  categorical  in  both.  And  the  meaning 
of  a  Hypothetical  Major  Premiss  (unless  it  is  a  mere 
arbitrary  convention  between  two  disputants,  to  the 
effect  that  the  Consequent  will  be  admitted  if  the 
Antecedent  is  proved,  or  that  the  Antecedent  will  be 
relinquished  if  the  Consequent  is  disproved),  can 
always  be  put  in  the  form  of  a  general  proposition, 
from  which,  with  the  Minor  Premiss  as  applying 


Conditional  Arguments.  219 

proposition,  a  conclusion   identical  with  the  original 
can  be  drawn  in  regular  Categorical  form. 
Thus  :— 

If  the  harbour  is  frozen,  the  ships  cannot  come  in. 
The  harbour  is  frozen. 
.•.  The  ships  cannot  come  in. 

This  is  a  Hypothetical  Syllogism,  Modus  Ponens. 
Express  the  Hypothetical  Major  in  the  form  of  the 
general  proposition  which  it  implies,  and  you  reach  a 
conclusion  (in  Barbara]  which  is  only  grammatically 
different  from  the  original. 

All  frozen  harbours  exclude  ships. 
The  harbour  is  frozen. 
.'.  It  excludes  ships. 

Again,  take  an  example  of  the  Modus  Tollens — 

If  rain  has  fallen,  the  streets  are  wet. 
The  streets  are  not  wet. 
.'.  Rain  has  not  fallen. 

This  is  reducible,  by  formulating  the  underlying 
proposition,  to  Camestres  or  Baroko  of  the  Second 
Figure. 

All  streets  rained  upon  are  wet. 

The  streets  are  not  wet. 
/.  They  are  not  streets  rained  upon. 

Hypothetical  Syllogisms  are  thus  reducible,  by 
merely  grammatical  change,1  or  by  the  statement  of 

1  It  may  be  argued  that  the  change  is  not  merely  grammatical, 
and  that  the  implication  of  a  general  proposition  in  a  hypothetical 
and  vice  -versa  is  a  strictly  logical  concern.  At  any  rate  such  an 
implication  exists,  whether  it  is  the  function  of  the  Grammarian 
or  the  Logician  to  expound  it. 


220  The  Interdependence  of  Propositions. 

self-evident  implications,  to  the  Categorical  form. 
And,  similarly,  any  Categorical  Syllogism  may  be 
reduced  to  the  Hypothetical  form.  Thus : — 

All  men  are  mortal. 
Socrates  is  a  man. 
.'.  Socrates  is  mortal. 

This  argument  is  not  different,  except  in  the  expression 
of  the  Major  and  the  Conclusion,  from  the  following  : — 

If  Socrates  is  a  man,  death  will  overtake  him. 
Socrates  is  a  man. 
.'.  Death  will  overtake  him. 

The  advantage  of  the  Hypothetical  form  in  argument 
is  that  it  is  simpler.  It  was  much  used  in  Mediaeval 
Disputation,  and  is  still  more  popular  than  the 
Categorical  Syllogism.  Perhaps  the  prominence  given 
to  Hypothetical  Syllogisms  as  syllogisms  in  Post- 
Renaissance  text-books  is  due  to  the  use  of  them  in 
the  formal  disputations  of  graduands  in  the  Universities. 
It  was  the  custom  for  the  Disputant  to  expound  his 
argument  in  this  form  : — 

If  so  and  so  is  the  case,  such  and  such  follows. 
So  and  so  is  the  case. 
.'.  Such  and  such  follows. 

To  which  the  Respondent  would  reply :  Accipio 
antecedentem,  nego  consequentiam,  and  argue  accordingly. 
Petrus  Hispanus  does  not  give  the  Hypothetical 
Syllogism  as  a  Syllogism  :  he  merely  explains  the  true 
law  of  Reason  and  Consequent  in  connexion  with  the 
Fallacia  Consequentis  in  the  section  on  Fallacies. 
(Summulcz.  Tractatus  Sextus.} 


Conditional  Arguments.  221 

II. — DISJUNCTIVE  SYLLOGISMS. 

A  Disjunctive  Syllogism  is  a  syllogism  in  which  the 
Major  Premiss  is  a  Disjunctive  Proposition,  i.e.,  one 
in  which  two  propositions  are  declared  to  be  mutually 
incompatible.  It  is  of  the  form  Either  A  is  B,  or  C  is 
D.1 

If  the  disjunction  between  the  alternatives  is  really 
complete,  the  form  implies  four  hypothetical  proposi- 
tions : — 

(1)  If  A  is  B,  C  is  not  D. 

(2)  If  A  is  not  B,  C  is  D. 

(3)  If  C  is  D,  A  is  not  B. 

(4)  If  C  is  not  D,  A  is  B. 

Suppose  then  that  an  antagonist  has  granted  you 
a  Disjunctive  Proposition,  you  can,  using  this  as  a 
Major  Premiss,  extract  from  him  four  different  Con- 
clusions, if  you  can  get  him  also  to  admit  the  requisite 
Minors.  The  Mode  of  two  of  these  is  technically 
called  Modus  Ponendo  Tollens,  the  mode  that  denies 
the  one  alternative  by  granting  the  other — A  is  B, 
therefore  C  is  not  D ;  C  is  D,  therefore  A  is  not  B. 
The  other  Mode  is  also  twice  open,  the  Modus 
Tollendo  Ponens — A  is  not  B,  therefore  C  is  D ;  C  is 
not  D,  therefore  A  is  B. 

Fallacy  is  sometimes  committed  through  the  Dis- 
junctive form  owing  to  the  fact  that  in  common  speech 
there  is  a  tendency  to  use  it  in  place  of  a  mere 

1  Some  logicians  prefer  the  form  Either  A  is,  or  B  is.  But  the 
two  alternatives  are  propositions,  and  if  "  A  is  "  represents  a  pro- 
position, the  "  is "  is  not  the  Syllogistic  copula.  If  this  is 
understood  it  does  not  matter :  the  analysis  of  the  alternative 
propositions  is  unessential. 


222  The  Interdependence  of  Propositions. 

hypothetical,  when  there  are  not  really  two  incom- 
patible alternatives.  Thus  it  may  be  said  "  Either  the 
witness  is  perjured,  or  the  prisoner  is  guilty,"  when  the 
meaning  merely  is  that  if  the  witness  is  not  perjured 
the  prisoner  is  guilty.  But  really  there  is  not  a  valid 
disjunction  and  a  correct  use  of  the  disjunctive  form, 
unless  four  hypotheticals  are  implied,  that  is,  unless 
the  concession  of  either  involves  the  denial  of  the 
other,  and  the  denial  of  either  the  concession  of  the 
other.  Now  the  prisoner  may  be  guilty  and  yet  the 
witness  be  perjured ;  so  that  two  of  the  four  hypo- 
theticals, namely — 

If  the  witness  is  perjured,  the  prisoner  is  not  guilty. 

If  the  prisoner  is  guilty,  the  witness  is  not  perjured — 
do  not  necessarily  hold.  If,  then,  we  would  guard 
against  fallacy,  we  must  always  make  sure  before 
assenting  to  a  disjunctive  proposition  that  there  is 
really  a  complete  disjunction  or  mutual  incompatibility 
between  the  alternatives. 


III. — THE  DILEMMA. 

A  Dilemma  is  a  combination  of  Hypothetical  and 
Disjunctive  propositions. 

The  word  has  passed  into  common  speech,  and  its 
ordinary  use  is  a  clue  to  the  logical  structure.  We  are 
said  to  be  in  a  dilemma  when  we  have  only  two  courses 
open  to  us  and  both  of  them  are  attended  by  unpleasant 
consequences.  In  argument  we  are  in  this  position 
when  we  are  shut  into  a  choice  between  two  admis- 
sions, and  either  admission  leads  to  a  conclusion  which 
we  do  not  like.  The  statement  of  the  alternatives  as 
the  consequences  hypothetically  of  certain  conditions 
is  the  major  premiss  of  the  dilemma :  once  we  admit 


Conditional  Arguments.  225 

that  the  relations  of  Antecedent  and  Consequent  are 
as  stated,  we  are  in  a  trap,  if  trap  it  is  :  we  are  on  the 
horns  of  the  dilemma,  ready  to  be  tossed  from  one  to 
the  other. 

For  example : — 

If  A  is  B,  A  is  C,  and  if  A  is  not  B,  A  is  D.  But  A 
either  is  or  is  not  B.  Therefore,  A  either  is  C  or  is  D. 

If  A  acted  of  his  own  motive,  he  is  a  knave ;  if  A 
did  not  act  of  his  own  motive,  he  is  a  catspaw.  But 
A  either  acted  of  his  own  motive  or  he  did  not. 
Thereupon  A  is  either  a  knave  or  a  catspaw. 

This  is  an  example  of  the  Constructive  Dilemma,  the 
iorm  of  it  corresponding  to  the  common  use  of  the 
word  as  a  choice  between  equally  unpleasant  alterna- 
tives. The  standard  example  is  the  dilemma  in  which 
the  custodians  of  the  Alexandrian  Library  are  said  to 
have  been  put  by  the  Caliph  Omar  in  640  A.D. 

If  your  books  are  in  conformity  with  the  Koran,  they 
are  superfluous;  if  they  are  at  variance  with 'it,  they 
are  pernicious.  But  they  must  either  be  in  conformity 
with  the  Koran  or  at  variance  with  it.  Therefore 
they  are  either  superfluous  or  pernicious. 

Where  caution  has  to  be  exercised  is  in  accepting 
the  clauses  of  the  Major.  We  must  make  sure  that 
the  asserted  relations  of  Reason  and  Consequent  really 
hold.  It  is  there  that  fallacy  is  apt  to  creep  in  and 
hide  its  head.  The  Alexandrian  Librarians  were  rash 
in  accepting  the  first  clause  of  the  conqueror's  Major : 
it  does  not  follow  that  the  books  are  superfluous  unless 
the  doctrines  of  the  Koran  are  not  merely  sound  but 
contain  all  that  is  worth  knowing.  The  propounder 
of  the  dilemma  covertly  assumes  this.  It  is  in  the 
ifaclity  that  it  affords  for  what  is  technically  known  as 


224  The  Interdependence  of  Propositions. 

Petitio  Principii  that  the  Dilemma  is  a  useful  instru- 
ment for  the  Sophist.  We  shall  illustrate  it  further 
under  that  head. 

What  is  known  as  the  Destructive  Dilemma  is  of  a 
somewhat  different  form.  It  proceeds  upon  the  denial 
of  the  Consequent  as  involving  the  denial  of  the 
Antecedent.  In  the  Major  you  obtain  the  admission 
that  if  a  certain  thing  holds,  it  must  be  followed  by  one 
or  other  of  two  consequences.  You  then  prove  by  way 
of  Minor  that  neither  of  the  alternatives  is  true.  The 
conclusion  is  that  the  antecedent  is  false. 

We  had  an  example  of  this  in  discussing  whether 
the  inference  in  the  Hypothetical  Syllogism  is  Im- 
mediate. Our  argument  was  in  this  form  : — 

If  the  inference  is  immediate,  it  must  be  drawn 
either  from  the  Major  alone  or  from  the  Minor  alone. 
But  it  cannot  be  drawn  from  the  Major  alone,  neither 
can  it  be  drawn  from  the  Minor  alone.  Therefore,  it  is 
not  immediate. 

In  this  form  of  Dilemma,  which  is  often  serviceable 
for  clearness  of  exposition,  we  must  as  in  the  other 
make  sure  of  the  truth  of  the  Major :  we  must  take 
care  that  the  alternatives  are  really  the  only  two 
open.  Otherwise  the  imposing  form  of  the  argument 
is  a  convenient  mask  for  sophistry.  Zeno's  famous 
dilemma,  directed  to  prove  that  motion  is  impossible, 
covers  a  petitio  principii. 

If  a  body  moves,  it  must  move  either  where  it  is  or 
where  it  is  not.  But  a  body  cannot  move  where  it 
is :  neither  can  it  move  where  it  is  not.  Conclu- 
sion, it  cannot  move  at  all,  i.e.,  Motion  is  impossible. 

The  conclusion  is  irresistible  if  we  admit  the  Major, 
because  the  Major  covertly  assumes  the  point  to  be 


Conditional  Arguments.  225 

proved.  In  truth,  if  a  body  moves,  it  moves  neither 
where  it  is  nor  where  it  is  not,  but  from  where  it  is  to 
where  it  is  not.  Motion  consists  in  change  of  place  : 
the  Major  assumes  that  the  place  is  unchanged,  that  is, 
that  there  is  no  motion. 


CHAPTER  VIII. 

FALLACIES    IN    DEDUCTIVE    ARGUMENT.—  PETITIO 
PR1NCIPII  AND  IGNORATIO  ELENCHI. 

THE  traditional  treatment  of  Fallacies  in  Logic  follows 
Aristotle's  special  treatise  Ilepi  CTO<£IO-TIK<OJ/  eXey^wv — 
Concerning  Sophistical  Refutations — Pretended  Dis- 
proofs— Argumentative  Tricks. 

Regarding  Logic  as  in  the  main  a  protection  against 
Fallacies,  I  have  been  going  on  the  plan  of  taking  each 
fallacy  in  connexion  with  its  special  safeguard,  and  in 
accordance  with  that  plan  propose  to  deal  here  with 
the  two  great  types  of  fallacy  in  deductive  argument. 
Both  of  them  were  recognised  and  named  by  Aristotle  : 
but  before  explaining  them  it  is  worth  while  to  indicate 
Aristotle's  plan  as  a  whole.  Some  of  his  Argumenta- 
tive Tricks  were  really  peculiar  to  Yes-and-No  Dialectic 
in  its  most  sportive  forms :  but  his  leading  types,  both 
Inductive  and  Deductive,  are  permanent,  and  his  plan 
as  a  whole  has  historical  interest.  Young  readers 
would  miss  them  from  Logic :  they  appeal  to  the 
average  argumentative  boy. 

He  divides  Fallacies  broadly  into  Verbal  Fallacies 
(•n-apa  ryv  At'£iv,  in  dictione),  and  Non- Verbal  Fallacies 
(e^co  rrjs  Ae'^ews,  extra  dictioneni}. 

The  first  class  are  mere  Verbal  Quibbles,  and  hardly 
deserve  serious  treatment,  still  less  minute  sub- 
divsiion.  The  world  was  young  when  time  was  spent 
(226) 


Fallacies  in  Deductive  Argument.  227 

upon  them.  Aristotle  names  six  varieties,  but  they 
all  turn  on  ambiguity  of  word  or  structure,  and  some 
of  them,  being  dependent  on  Greek  syntax,  cannot 
easily  be  paralleled  in  another  tongue. 

(1)  Ambiguity  of  word  (o/xcwv/ua).     As  if  one  were 
to  argue:  "All  cold  can  be  expelled  by  heat:  John's 
illness  is  a  cold  :  therefore  it  can  be  expelled  by  heat". 
Or :  "  Some  afflictions  are  cheering,  for  afflictions  are 
sometimes  light,  and  light  is  always  cheering".     The 
serious  confusion    of  ambiguous    words    is    met    by 
Definition,  as  explained  at  length  in  pt.  ii.  c.  i. 

(2)  Ambiguity  of  structure  (d/A</>i/?oAia). 

' '  What  he  was  beaten  with  was  what  I  saw  him 
beaten  with :  what  I  saw  him  beaten  with  was  my 
eye  :  therefore,  what  he  was  beaten  with  was  my  eye." 

"  How  do  you  do  ?"  "Do?  Do  what?"  "I  mean, 
how  do  you  feel  ? "  "  How  do  I  feel  ?  With  my 
fingers,  of  course ;  but  I  can  see  very  well."  "  No, 
no  ;  I  mean,  how  do  you  find  yourself?  "  "  Then  why 
did  you  not  say  so  ?  I  never  exactly  noticed,  but  I 
will  tell  you  next  time  I  lose  myself." 

(3)  Illicit  conjunction  (a-vvOfo-Ls). 

Socrates  is  good.  Socrates  is  a  musician.  There- 
fore Socrates  is  a  good  musician. 

(4)  Illicit  disjunction  (8iai/oe<ng). 

Socrates  is  a  good  musician.  Therefore  he  is  a  good 
man. 

(5)  Ambiguity    of  pronunciation    (TrpotrwSia,    fallacia 

accentus}. 

Analogies  to  words  that  differ  only  in  accent,  such 
as  ov  and  ov,  may  be  found  in  differences  of  pronuncia- 
tion. "  Hair  very  thick,  sir,"  said  a  barber  to  a 
customer,  whose  hair  was  bushy,  but  beginning  to  turn 
grey.  "  Yes,  I  daresay.  But  I  would  rather  have  it 


228  The  Interdependence  of  Propositions. 

thick  than  thin."  "  Ah,  too  thick  to-day,  sir."  "  But 
I  don't  want  to  dye  it."  "  Excuse  me,  sir,  I  mean  the 
hair  of  the  hatmosphere,  t-o-d-a-y,  to-day." 

"  He  said,  saddle  me  the  ass.  And  they  saddled 
him." 

(6)  Ambiguity  of  inflexion  (cr^/Ao,  rrj<s  Ac'£e<os,  Figura 
dictionis). 

This  is  not  easy  to  make  intelligible  in  English. 
The  idea  is  that  a  termination  may  be  ambiguously 
interpreted,  a  neuter  participle,  e.g.,  taken  for  an  active. 
Thus:  "George  is  ailing".  "Doing  what,  did  you 
say  ?  Ailing  ?  What  is  he  ailing  ?  Ginger-aleing  ?  " 

Non-Verbal  Fallacies,  or  Fallacies  in  thought,  are 
a  more  important  division.  Aristotle  distinguishes 
seven. 

Of  these,  three  are  comparatively  unimportant  and 
trifling.  One  of  them,  known  to  the  Schoolmen  as 
Fallada  Plurium  Interrogationum,  was  peculiar  to 
Interrogative  disputation.  It  is  the  trick  of  putting 
more  than  one  question  as  one,  so  that  a  simple  Yes 
commits  the  respondent  to  something  implied.  "  Have 
you  left  off  beating  your  father  ?  "  If  you  answer  Yes, 
that  implies  that  you  have  been  in  the  habit  of  beating 
him.  "  Has  the  practice  of  excessive  drinking  ceased 
in  your  part  of  the  country  ?  "  Such  questions  were 
unfair  when  the  Respondent  could  answer  only  Yes 
or  No  The  modern  disputant  who  demands  a  plain 
answer  Yes  or  No,  is  sometimes  guilty  of  this  trick. 

Two  others,  the  fallacies  known  as  A  dicto  simplidter 
ad  dictum  secundum  quid,  and  A  dicto  secundum  quid  ad 
dictum  simplidter,  are  as  common  in  modern  dialectic  as 
they  were  in  ancient.  The  trick,  conscious  or  uncon- 
scious, consists  in  getting  assent  to  a  statement  with  a 
qualification  and  proceeding  to  argue  as  if  it  had  been 


Fallacies  in  Deductive  Argument.  229 

conceded  without  qualification,  and  vice  versa.  For 
example,  it  being  admitted  that  culture  is  good,  a 
disputant  goes  on  to  argue  as  if  the  admission  applied 
to  some  sort  of  culture  in  special,  scientific,  aesthetic, 
philosophical  or  moral.  The  fallacy  was  also  known 
as  Fallacia  Accidentis.  Proving  that  the  Syllogism  is 
useless  for  a  certain  purpose,  and  then  claiming  to 
have  proved  that  it  is  useless  for  any  purpose  is  another 
example.  Getting  a  limited  admission  and  then 
extending  it  indefinitely  is  perhaps  the  more  common 
of  the  two  forms.  It  is  common  enough  to  deserve  a 
shorter  name. 

The  Fallacia  Consequentis,  or  Non-Sequitur,  which 
consists  specially  in  ignoring  the  possibility  of  a 
plurality  of  causes,  has  already  been  partly  explained 
in  connexion  with  the  Hypothetical  Syllogism,  and 
will  be  explained  further  in  the  Logic  of  Induction. 

Post  hoc  ergo  proper  hoc  is  a  purely  Inductive  Fallacy, 
and  will  be  explained  in  connexion  with  the  Experi- 
mental Methods. 

There  remain  the  two  typical  Deductive  Fallacies, 
Petitio  Principii  (Surreptitious  Assumption)  and»Igno- 
ratio  Elenchi  (Irrelevant  Argument)  about  which  we 
must  speak  more  at  length. 

The  phrase  of  which  Petitio  Principii  or  Begging  the 
Question  is  a  translation — TO  kv  apxfi  a-iTtia-Oai — was 
applied  by  Aristotle  to  an  argumentative  trick  in 
debate  by  Question  and  Answer.  The  trick  consisted 
in  taking  for  granted  a  proposition  necessary  to  the 
refutation  without  having  obtained  the  admission  of  it. 
Another  expression  for  the  same  thing — TO  ev  apxfi 
Xapfidvew — taking  the  principle  for  granted — is  more 
descriptive. 

Generally    speaking,    Aristotle    says,    Begging    the 


230  The  Interdependence  of  Propositions. 

Question  consists  in  not  demonstrating  the  theorem. 
It  would  be  in  accordance  with  this  general  description 
to  extend  the  name  to  all  cases  of  tacitly  or  covertly, 
unwittingly  to  oneself  or  to  one's  opponent,  assuming 
any  premiss  necessary  to  the  conclusion.  It  is  the 
fallacy  of  Surreptitious  Assumption,  and  all  cases  of 
Enthymematic  or  Elliptical  argument,  where  the 
unexpressed  links  in  the  chain  of  argument  are  not 
fully  understood,  are  examples  of  it.  By  contrast,  the 
articulate  and  explicit  Syllogism  is  an  Expositio  Prindpii. 
The  only  remedy  for  covert  assumptions  is  to  force 
them  into  the  light.1 

Ignoratio  Elenchi,  ignoring  the  refutation  (TOV 
eAeyx°u  ayvoia),  is  simply  arguing  beside  the  point,  dis- 
tracting the  attention  by  irrelevant  considerations.  It 
often  succeeds  by  proving  some  other  conclusion  which 
is  not  the  one  in  dispute,  but  has  a  superficial  resem- 
blance to  it,  or  is  more  or  less  remotely  connected  with 
it. 

It  is  easier  to  explain  what  these  fallacies  consist  in 
than  to  illustrate  them  convincingly.  It  is  chiefly  in 
long  arguments  that  the  mischief  is  done.  "  A  Fallacy," 
says  Whately,  "  which  when  stated  barely  in  a  few 
sentences  would  not  deceive  a  child,  may  deceive  half 
the  world  if  diluted  in  a  quarto  volume."  Very  rarely 
is  a  series  of  propositions  put  before  us  in  regular  form 
and  order,  all  bearing  on  a  definite  point.  A  certain 
conclusion  is  in  dispute,  not  very  definitely  formulated 
perhaps,  and  a  mixed  host  of  considerations  are 
tumbled  out  before  us.  If  we  were  perfectly  clear- 


1  Cp.  Mr.    Sidgwick's  instructive  treatise  on   Fallacies,   Inter- 
national Scientific  Series,  p.  199. 


Fallacies  in  Deductive  Argument.  231 

headed  persons,  capable  of  protracted  concentration  of 
attention,  incapable  of  bewilderment,  always  on  the 
alert,  never  in  a  hurry,  never  over-excited,  absolutely 
without  prejudice,  we  should  keep  our  attention  fixed 
upon  two  things  while  listening  to  an  argument,  the 
point  to  be  proved,  and  the  necessary  premisses.  We 
should  hold  the  point  clearly  in  our  minds,  and  watch 
indefatigably  for  the  corroborating  propositions.  But 
none  of  us  being  capable  of  this,  all  of  us  being  subject 
to  bewilderment  by  a  rapid  whirl  of  statements,  and  all 
of  us  biased  more  or  less  for  or  against  a  conclusion, 
the  sophist  has  facilities  for  doing  two  things — taking 
for  granted  that  he  has  stated  the  required  premisses 
(fietitio prindpii),  and  proving  to  perfect  demonstration 
something  which  is  not  the  point  in  dispute,  but  which 
we  are  willing  to  mistake  for  it  (ignoratio  elenchi}. 

It  is  chiefly  in  the  heat  of  argument  that  either 
Petitio  or  Ignoratio  succeeds.  When  a  fallacy  con- 
tinues to  perplex  us  in  cold  blood,  it  must  have  in  its 
favour  either  some  deeply-rooted  prejudice  or  some 
peculiar  intricacy  in  the  language  used,  or  some 
abstruseness  in  the  matter.  If  we  are  not  familiar 
with  the  matter  of  the  argument,  and  have  but  a  vague 
hold  of  the  words  employed,  we  are,  of  course,  much 
more  easily  imposed  upon. 

The  famous  Sophisms  of  antiquity  show  the  fascina- 
tion exercised  over  us  by  proving  something,  no  matter 
how  irrelevant.  If  certain  steps  in  an  argument  are 
sound,  we  seem  to  be  fascinated  by  them  so  that  we 
cannot  apply  our  minds  to  the  error,  just  as  our  senses 
are  fascinated  by  an  expert  juggler.  We  have  seen 
how  plausibly  Zeno's  argument  against  the  possibility 
of  motion  hides  a  Petitio :  the  Fatalist  Dilemma  is 
another  example  of  the  same  sort. 


232  The  Interdependence  of  Propositions. 

If  it  is  fated  that  you  die,  you  will  die  whether  you 
call  in  a  doctor  or  not,  and  if  it  is  fated  that  you  will 
recover,  you  will  recover  whether  you  call  in  a  doctor 
or  not.  But  it  must  be  fated  either  that  you  die  or 
that  you  recover.  Therefore,  you  will  either  die  or 
recover  whether  you  call  in  a  doctor  or  not. 

Here  it  is  tacitly  assumed  in  the  Major  Premiss  that 
the  calling  in  of  a  doctor  cannot  be  a  link  in  the  fated 
chain  of  events.  In  the  statement  of  both  the  alter- 
native conditions,  it  is  assumed  that  Fate  does  not  act 
through  doctors,  and  the  conclusion  is  merely  a 
repetition  of  this  assumption,  a  verbal  proposition 
after  an  imposing  show  of  argument.  "  If  Fate  does 
not  act  through  doctors,  you  will  die  whether  you  call 
in  a  doctor  or  not." 

The  fallacy  in  this  case  is  probably  aided  by  our 
veneration  for  the  grand  abstraction  of  Fate  and  the 
awful  idea  of  Death,  which  absorbs  our  attention  and 
takes  it  away  from  the  artful  Petitio, 

The  Sophism  of  Achilles  and  the  Tortoise  is  the 
most  triumphant  of  examples  of  Ignoratio  Elenchi. 

The  point  that  the  Sophism  undertakes  to  prove  is 
that  Achilles  can  never  overtake  a  Tortoise  once  it 
has  a  certain  start :  what  it  really  proves,  and  proves 
indisputably,  is  that  he  cannot  overtake  the  Tortoise 
within  a  certain  space  or  time. 

For  simplicity  of  exposition,  let  us  assume  that  the 
Tortoise  has  100  yards  start  and  that  Achilles  runs  ten 
times  as  fast.  Then,  clearly,  Achilles  will  not  come 
up  with  it  at  the  end  of  100  yards,  for  while  he  has  run 
100,  the  Tortoise  has  run  10  ;  nor  at  the  end  of  no,  for 
then  the  Tortoise  has  run  i  more  ;  nor  at  the  end  of  1 1 1 , 
for  then  the  Tortoise  has  run  T^  more ;  nor  at  the  end 
of  iiiTV>  for  then  the  Tortoise  has  gained  -^-$  more. 


Fallacies  in  Deductive  Argument.  233 

So  while  Achilles  runs  this  yj^,  the  Tortoise  runs 
p^.  ;  while  he  runs  the  y^,  it  runs  ^J-^.  Thus 
it  would  seem  that  the  Tortoise  must  always  keep 
ahead  :  he  can  never  overtake  it. 

But  the  conclusion  is  only  a  confusion  of  ideas  :  all 
that  is  really  proved  is  that  Achilles  will  not  overtake 
the  Tortoise  while  running 

100  +  10  +  i  +        +          +  +  etc- 


That  is,  that  he  will  not  overtake  it  till  he  has  com- 
pleted the  sum  of  this  series,  in-J-  yards.  To  prove 
this  is  an  ignoratio  elenchi  ;  what  the  Sophist  undertakes 
to  prove  is  that  Achilles  will  never  overtake  it,  and  he 
really  proves  that  Achilles  passes  it  between  the  mth 
and  1  1  2th  yards. 

The  exposure  of  this  sophism  is  an  example  also  of 
the  value  of  a  technical  term.  All  attempts  to  expose 
it  without  using  the  term  Ignoratio  Elenchi  or  some- 
thing equivalent  to  it,  succeed  only  in  bewildering  the 
student.  It  is  customary  to  say  that  the  root  of  the 
fallacy  lies  in  assuming  that  the  sum  of  an  infinite 
series  is  equal  to  infinity.  This  profound  error  may  be 
implied  :  but  if  any  assumption  so  hard  to  understand 
were  really  required,  the  fallacy  would  have  little  force 
with  the  generality. 

It  has  often  been  argued  that  the  Syllogism  involves 
a  petitio  principii,  because  the  Major  Premiss  contains 
the  Conclusion,  and  would  not  be  true  unless  the 
Conclusion  were  true.  But  this  is  really  an  Ignoratio 
Elenchi.  The  fact  adduced,  that  the  Major  Premiss 
contains  the  Conclusion,  is  indisputable  ;  but  this  does 
not  prove  the  Syllogism  guilty  of  Petitio.  Petitio 
principii  is  an  argumentative  trick,  a  conscious  or 
unconscious  act  of  deception,  a  covert  assumption,  and 


234  The  Interdependence  of  Propositions. 

the  Syllogism,  so  far  from  favouring  this,  is  an  expositio 
principii,  an  explicit  statement  of  premisses  such  that, 
if  they  are  true,  the  conclusion  is  true.  The  Syllogism 
merely  shows  the  interdependence  of  premisses  and 
conclusion  ;  its  only  tacit  assumption  is  the  Dictum  de 
Omni. 

If,  indeed,  an  opponent  challenges  the  truth  of  the 
conclusion,  and  you  adduce  premisses  necessarily 
containing  it  as  a  refutation,  that  is  an  ignoratio  elenchi 
unless  your  opponent  admits  those  premisses.  If  he 
admits  them  and  denies  the  conclusion,  you  convict 
him  of  inconsistency,  but  you  do  not  prove  the  truth 
of  the  conclusion.  Suppose  a  man  to  take  up  the 
position :  "  I  am  not  mortal,  for  I  have  procured  the 
elixir  vita  ".  You  do  not  disprove  this  by  saying,  "  All 
men  are  mortal,  and  you  are  a  man".  In  denying 
that  he  is  mortal,  he  denies  that  all  men  are  mortal. 
Whatever  is  sufficient  evidence  that  he  is  not  mortal, 
is  sufficient  evidence  that  all  men  are  not  mortal. 
Perhaps  it  might  be  said  that  in  arguing,  "  All  men 
are  mortal,  and  you  are  a  man,"  it  is  not  so  much 
ignoratio  elenchi  as  petitio  principit  that  you  commit. 
But  be  it  always  remembered  that  you  may  commit 
both  fallacies  at  once.  You  may  both  argue  beside 
the  point  and  beg  the  question  in  the  course  of  one 
and  the  same  argument. 


CHAPTER  IX. 

FORMAL  OR  ARISTOTELIAN  INDUCTION.— INDUCTIVE 
ARGUMENT. 

THE  distinction  commonly  drawn  between  Deduction 
and  Induction  is  that  Deduction  is  reasoning  from 
general  to  particular,  and  Induction  reasoning  from 
particular  to  general. 

But  it  is  really  only  as  modes  of  argumentation  that 
the  two  processes  can  be  thus  clearly  and  fixedly  opposed. 
The  word  Induction  is  used  in  a  much  wider  sense 
when  it  is  the  title  of  a  treatise  on  the  Methods  of 
Scientific  Investigation,  It  is  then  used  to  cover  all 
the  processes  employed  in  man's  search  into  the 
system  of  reality;  and  in  this  search  deduction  is 
employed  as  well  as  induction  in  the  narrow  sense. 

We  may  call  Induction  in  the  narrow  sense  Formal 
Induction  or  Inductive  Argument,  or  we  may  simply 
call  it  Aristotelian  Induction  inasmuch  as  it  was  the 
steps  of  Inductive  argument  that  Aristotle  formulated, 
and  for  which  he  determined  the  conditions  of  validity. 

Let  us  contrast  it  with  Deductive  argument.  In 
this  the  questioner's  procedure  is  to  procure  the  admis- 
sion of  a  general  proposition  with  a  view  to  forcing 
the  admission  of  a  particular  conclusion  which  is  in 
dispute.  In  Inductive  argument,  on  the  other  hand,  it 
is  a  general  proposition  that  is  in  dispute,  and  the 

(235) 


236  The  Interdependence  of  Propositions. 

procedure  is  to  obtain  the  admission  of  particular  cases 
with  a  view  to  forcing  the  admission  of  this  general 
proposition. 

Let  the  question  be  whether  All  horned  animals 
ruminate.  You  engage  to  make  an  opponent  admit 
this.  How  do  you  proceed  ?  You  ask  him  whether 
he  admits  it  about  the  various  species.  Does  the  ox 
ruminate?  The  sheep?  The  goat?  And  so  on. 
The  bringing  in  of  the  various  particulars  is  the  induc- 
tion (eTraytoy^). 

When  is  this  inductive  argument  complete  ?  When 
is  the  opponent  bound  to  admit  that  all  horned  animals 
ruminate  ?  Obviously,  when  he  has  admitted  it  about 
every  one.  He  must  admit  that  he  has  admitted  it 
about  every  one,  in  other  words,  that  the  particulars 
enumerated  constitute  the  whole,  before  he  can  be  held 
bound  in  consistency  to  admit  it  about  the  whole. 

The  condition  of  the  validity  of  this  argument  is 
ultimately  the  same  with  that  of  Deductive  argument, 
the  identity  for  purposes  of  predication  of  a  generic 
whole  with  the  sum  of  its  constituent  parts.  The 
Axiom  of  Inductive  Argument  is,  What  is  predicated  of 
every  one  of  the  parts  is  predicable  of  the  whole.  This  is 
the  simple  converse  of  the  Axiom  of  Deductive  argu- 
ment, the  Dictum  de  Omni,  "  What  is  predicated  of  the 
whole  is  predicable  about  every  one  of  the  parts". 
The  Axiom  is  simply  convertible  because  for  purposes 
of  predication  generic  whole  and  specific  or  individual 
parts  taken  all  together  are  identical. 

Practically  in  inductive  argument  an  opponent  is 
worsted  when  he  cannot  produce  an  instance  to  the 
contrary.  Suppose  he  admits  the  predicate  in  question 
to  be  true  of  this,  that  and  the  other,  but  denies  that 
this,  that  and  the  other  constitute  the  whole  class  in 


Formal  or  Aristotelian  Induction.  237 

question,  he  is  defeated  in  common  judgment  if  he 
cannot  instance  a  member  of  the  class  about  which  the 
predicate  does  not  hold.  Hence  this  mode  of  induction 
became  technically  known  as  Indudio  per  enumerationem 
simplicem  ubi  non  reperitur  instantia  contradictoria. 
When  this  phrase  is  applied  to  a  generalisation  of  fact, 
Nature  or  Experience  is  put  figuratively  in  the  position 
of  a  Respondent  unable  to  contradict  the  inquirer. 

Such  in  plain  language  is  the  whole  doctrine  of 
Inductive  Argument.  Aristotle's  Inductive  Syllogism 
is,  in  effect,  an  expression  of  this  simple  doctrine 
tortuously  in  terms  of  the  Deductive  Syllogism.  The 
great  master  was  so  enamoured  of  his  prime  invention 
that  he  desired  to  impress  its  form  upon  everything  : 
otherwise,  there  was  no  reason  for  expressing  the  process 
of  Induction  syllogistically.  Here  is  his  description  of 
the  Inductive  Syllogism  :  — 

"  Induction,  then,  and  the  Inductive  Syllogism,  consists 
in  syllogising  one  extreme  with  the  middle  through  the 
other  extreme.  For  example,  if  B  is  middle  to  A  and  C,  to 
prove  through  C  that  A  belongs  to  B."  x 

This  may  be  interpreted  as  follows  :  Suppose  a 
general  proposition  is  in  dispute,  and  that  you  wish  to 
make  it  good  by  obtaining  severally  the  admission  of 
all  the  particulars  that  it  sums  up.  The  type  of  a 
general  proposition  in  Syllogistic  terminology  is  the 
Major  Premiss,  All  M  is  P.  What  is  the  type  of  the 
particulars  that  it  sums  up  ?  Obviously,  the  Con- 
clusion, S  is  P.  This  particular  is  contained  in  the 
Major  Premiss,  All  M  is  P  ;  its  truth  is  accepted  as 


/J.fv  olv  eVri  Kal  6  e|  eTraywyTjs  <rv\\oyiorfj.bs  rb  Stct  rov 
erepou  Q&repov  &Kpov  r<£  /Jieffy  (rv\\o'yicrao'0ai  •  Qtlov  el  riav  A  T  fjifffov 
rb  B,  Sta  rov  T  Sel^ou  rb  A  r$  B  vtrdpxov.  (An.  Prior.,  ii.  23.) 


238  The  Interdependence  of  Propositions* 

contained  in  the  truth  of  All  M  is  P.  S  is  one  of  the 
parts  of  the  generic  whole  M  ;  one  of  the  individuals  or 
species  contained  in  the  class  M.  If  you  wish,  then, 
to  establish  P  of  All  M  by  Induction,  you  must  estab- 
lish P  of  all  the  parts,  species,  or  individuals  contained 
in  M,  that  is,  of  all  possible  Sj  /  you  must  make  good 
that  this,  that  and  the  other  S  is  P,  and  also  that  this, 
that  and  the  other  S  constitute  the  whole  of  M. 
You  are  then  entitled  to  conclude  that  All  M  is  P  :  you 
have  syllogised  one  Extreme  with  the  Middle  through 
the  other  Extreme.  The  formal  statement  of  these 
premisses  and  conclusion  is  the  Inductive  Syllogism. 

This,  that  and  the  other  S  is  P,  Major. 
This,  that  and  the  other  S  is  all  M,  Minor. 
.'.  All  M  is  P,  Conclusion. 

This,  that  and  the  other  magnet  (i.e.,  magnets  indivi- 
dually) attract  iron. 
This,  that  and  the  other  magnet  (i.e.,  the  individuals 

separately  admitted)  are  all  magnets. 
/.  All  magnets  attract  iron. 

This,  that  and  the  other  S  being  simply  convertible 
with  All  M,  you  have  only  to  make  this  conversion 
and  you  have  a  syllogism  in  Barbara  where  this,  that 
and  the  other  S  figures  as  the  Middle  Term. 

The  practical  value  of  this  tortuous  expression  is  not 
obvious.  Mediaeval  logicians  shortened  it  into  what 
was  known  as  the  Inductive  Enthymeme :  "  This, 
that  and  the  other,  therefore  all,"  an  obvious  conclu- 
sion when  this,  that  and  the  other  constitute  all.  It 
is  merely  an  evidence  of  the  great  master's  intoxication 
with  his  grand  invention.  It  is  a  proof  also  that 
Aristotle  really  looked  at  Induction  from  the  point  of 
view  of  Interrogative  Dialectic.  His  question  was, 


Formal  or  Aristotelian  Induction.  239 

When  is  a  Respondent  bound  to  admit  a  general 
conclusion  ?  And  his  answer  was,  When  he  has 
admitted  a  certain  number  of  particulars,  and  cannot 
deny  that  those  particulars  constitute  the  whole  whose 
predicate  is  in  dispute.  He  was  not  concerned 
primarily  with  the  analysis  of  the  steps  of  an  inquirer 
generalising  from  Nature. 


' 

BOOK     II. 

INDUCTIVE  LOGIC,  OR  THE  LOGIC  OF  SCIENCE. 


16 


INTRODUCTION. 

PERHAPS  the  simplest  way  of  disentangling  the  leading 
features  of  the  departments  of  Logic  is  to  take  them 
in  relation  to  historical  circumstances.  These  features 
are  writ  large,  as  it  were,  in  history.  If  we  recognise 
that  all  bodies  of  doctrine  have  their  origin  in  practical 
needs,  we  may  conceive  different  ages  as  controlled 
each  by  a  distinctive  spirit,  which  issues  its  mandate 
to  the  men  of  the  age,  assigning  to  them  their  distinc- 
tive work. 

The  mandate  issued  to  the  age  of  Plato  and  Aristotle 
was  Bring  your  beliefs  into  harmony  one  with  another. 
The  Aristotelian  Logic  was  framed  in  response  to  this 
order  :  its  main  aim  was  to  devise  instruments  for 
making  clear  the  coherence,  the  concatenation,  the 
mutual  implication  of  current  beliefs. 

The  mandate  of  the  Mediaeval  Spirit  was  Bring  your 
beliefs  into  harmony  with  dogma.  The  mediaeval  logic 
was  contracted  from  Aristotle's  under  this  impulse. 
Induction  as  conceived  by  him  was  neglected,  allowed  • 
to  dwindle,  almost  to  disappear  from  Logic.  Greater 
prominence  was  given  to  Deduction. 

Then  as  Dogmatic  Authority  became  aggressive, 
and  the  Church  through  its  officials  claimed  to  pro- 
nounce on  matters  outside  Theology,  a  new  spirit  was 
roused,  the  mandate  of  which  was,  Bring  your  beliefs 
into  harmony  with  facts.  It  was  under  this  impulse  that 
(243) 


244         Inductive  Logic,  or  the  Logic  of  Science. 

a  body  of  methodical  doctrine  vaguely  called  Induction 
gradually  originated. 

In  dealing  with  the  genesis  of  the  Old  Logic,  we 
began  with  Aristotle.  None  can  dispute  his  title 
to  be  called  its  founder.  But  who  was  the  founder 
of  the  New  Logic  ?  In  what  circumstances  did  it 
originate  ? 

The  credit  of  founding  Induction  is  usually  given 
to  Francis  Bacon,  Lord  Verulam.  That  great  man 
claimed  it  for  himself  in  calling  his  treatise  on  the 
Interpretation  of  Nature  the  Novum  Organum.  The 
claim  is  generally  conceded.  Reid's  account  of  the 
matter  represents  the  current  belief  since  Bacon's  own 
time. 

"  After  man  had  laboured  in  the  search  of  truth 
near  two  thousand  years  by  the  help  of  Syllogisms, 
[Lord]  Bacon  proposed  the  method  of  INDUCTION  as  a 
more  effectual  engine  for  that  purpose.  His  Novum 
Organum  gave  a  new  turn  to  the  thoughts  and  labours 
of  the  inquisitive,  more  remarkable  and  more  useful 
than  that  which  the  Organon  of  Aristotle  had  given 
before,  and  may  be  considered  as  a  second  grand  era 
in  the  progress  of  human  nature.  .  .  .  Most  arts  have 
been  reduced  to  rules  after  they  had  been  brought  to  a 
considerable  degree  of  perfection  by  the  natural  saga- 
city of  artists ;  and  the  rules  have  been  drawn  from 
the  best  examples  of  the  art  that  had  been  before 
exhibited ;  but  the  art  of  philosophical  induction  was 
delineated  by  [Lord]  Bacon  in  a  very  ample  manner 
before  the  world  had  seen  any  tolerable  example 
of  it."1 

There  is  a  radical  misconception  here,  which,  for 
reasons  that  I  hope  to  make  plain,  imperatively  needs 

1  Hamilton's  Reid,  p.  712. 


Introduction.  245 

to  be  cleared  up.  It  obscures  the  very  essence  of 
"  philosophical  induction  ". 

There  are  three  ways  in  which  movement  in  any 
direction  may  be  helped  forward,  Exhortation,  Example, 
and  Precept.  Exhortation :  a  man  may  exhort  to 
the  practice  of  an  art  and  thereby  give  a  stimulus. 
Example :  he  may  practise  the  art  himself,  and  show 
by  example  how  a  thing  should  be  done.  Precept :  he 
may  formulate  a  clear  method,  and  so  make  plain  how 
to  do  it.  Let  us  see  what  was  Bacon's  achievement 
in  each  of  those  three  ways. 

Undoubtedly  Bacon's  powerful  eloquence  and  high 
political  position  contributed  much  to  make  the  study 
of  Nature  fashionable.  He  was  high  in  place  and 
great  in  intellect,  one  of  the  commanding  personalities 
of  his  time.  Taking  "all  knowledge  for  his  province," 
though  study  was  really  but  his  recreation,  he  sketched 
out  a  plan  of  universal  conquest  with  a  clearness  and 
confidence  that  made  the  mob  eager  to  range  them- 
selves under  his  leadership.  He  was  the  magnificent 
demagogue  of  science.  There  had  been  champions  of 
"  Induction"  before  him,  but  they  had  been  compara- 
tively obscure  and  tongue-tied. 

While,  however,  we  admit  to  the  full  the  great 
services  of  this  mighty  advocate  in  making  an  "  Induc- 
tive" method  popular,  we  should  not  forget  that  he 
had  pioneers  even  in  hortatory  leadership.  His 
happiest  watchword,  the  Interpretation  of  Nature,  as 
distinguished  from  the  Interpretation  of  Authoritative 
Books,  was  not  of  his  invention.  If  we  read  Whewell's 
History  of  the  Inductive  Sciences,  we  shall  find  that 
many  before  him  had  aspired  to  "  give  a  new  turn  to 
the  labours  of  the  inquisitive,"  and  in  particular  to 
substitute  inquisition  for  disquisition. 


246         Inductive  Logic,  or  the  Logic  of  Science. 

One  might  compile  from  Whewell  a  long  catalogue 
of  eminent  men  before  Bacon  who  held  that  the  study 
of  Nature  was  the  proper  work  of  the  inquisitive  : 
Leonardo  da  Vinci  (1452-1519),  one  of  the  wonders  of 
mankind  for  versatility,  a  miracle  of  excellence  in  many 
things,  painter,  sculptor,  engineer,  architect,  astro- 
nomer, and  physicist;  Copernicus  (1473-1543),  the 
author  of  the  Heliocentric  theory;  Telesius  (1508- 
1588),  a  theoretical  reformer,  whose  De  Rerum  Natura 
(1565)  anticipated  not  a  little  of  the  Novum  Organum  ; 
Cesalpinus  (1520-1603),  the  Botanist;  Gilbert  (1540- 
1603),  the  investigator  of  Magnetism.  By  all  these 
men  experiment  and  observation  were  advocated  as  the 
only  way  of  really  increasing  knowledge.  They  all 
derided  mere  book-learning.  The  conception  of  the 
world  of  sense  as  the  original  MS.  of  which  systems  of 
philosophy  are  but  copies,  was  a  familiar  image  with 
them.  So  also  was  Bacon's  epigrammatic  retort  to 
those  who  wish  to  rest  on  the  wisdom  of  the  ancients, 
that  antiquity  is  the  youth  of  the  world  and  that  we 
are  the  true  ancients.  «'  We  are  older,"  said  Giordano 
Bruno,  "  and  have  lived  longer  than  our  predecessors." 

This  last  argument,  indeed,  is  much  older  than  the 
sixteenth  century.  It  was  used  by  the  Doctor 
Mirabilis  of  the  thirteenth,  the  Franciscan  Friar, 
Roger  Bacon  (1214-1292).  "The  later  men  are,  the 
more  enlightened  they  are ;  and  wise  men  now  are 
ignorant  of  much  the  world  will  some  day  know."  The 
truth  is  that  if  you  are  in  search  of  a  Father  for 
Inductive  Philosophy,  the  mediaeval  friar  has  better 
claims  than  his  more  illustrious  namesake.  His 
enthusiasm  for  the  advancement  of  learning  was  not 
less  nobly  ambitious  and  far-reaching,  and  he  was 
himself  an  ardent  experimenter  and  inventor.  His 


Introduction.  247 

Opus  Majus — an  eloquent  outline  of  his  projects  for  a 
new  learning,  addressed  in  1265  to  Pope  Clement  IV., 
through  whom  he  offered  to  give  to  the  Church  the 
empire  of  the  world  as  Aristotle  had  given  it  to 
Alexander — was  almost  incredibly  bold,  comprehensive 
and  sagacious.  Fixing  upon  Authority,  Custom, 
Popular  Opinion,  and  the  Pride  of  Supposed  Knowledge, 
as  the  four  causes  of  human  ignorance,  he  urged  a 
direct  critical  study  of  the  Scriptures,  and  after  an 
acute  illustration  of  the  usefulness  of  Grammar  and 
Mathematics  (widely  interpreted),  concluded  with 
Experimental  Science  as  the  great  source  of  human 
knowledge.  I  have  already  quoted  (p.  15)  the  Friar's 
distinction  between  the  two  modes  of  Knowing, 
Argument  and  Experience,  wherein  he  laid  down  that 
it  is  only  experience  that  makes  us  feel  certain.  It 
were  better,  he  cried  in  his  impatience,  to  burn  Aristotle 
and  make  a  fresh  start  than  to  accept  his  conclusions 
without  inquiry. 

Experimental  Science,  the  sole  mistress  of  Specu- 
lative Science,  has  three  great  Prerogatives  among 
other  parts  of  Knowledge.  First,  she  tests  by  experi- 
ment the  noblest  conclusions  of  all  other  sciences. 
Next,  she  discovers  respecting  the  notions  which  other 
sciences  deal  with,  magnificent  truths  to  which  these 
sciences  can  by  no  means  attain.  Her  third  dignity 
is  that  she  by  her  own  power  and  without  respect  to 
other  sciences  investigates  the  secret  of  Nature. 

So  far,  then,  as  Exhortation  goes,  King  James's 
great  lawyer  and  statesman  was  not  in  advance  of 
Pope  Clement's  friar.  Their  first  principle  was  the 
same.  It  is  only  by  facts  that  theories  can  be  tested. 
Man  must  not  impose  his  own  preconceptions 
(anticipationes  mentis]  on  nature.  Man  is  only  the 


248         Inductive  Logic,  or  the  Logic  of  Science. 

interpreter  of  nature.  Both  were  also  at  one  in  holding 
that  the  secrets  of  nature  could  not  be  discovered  by 
discussion,  but  only  by  observation  and  experiment. 

Francis  Bacon,  however,  went  beyond  all  his  prede- 
cessors in  furnishing  an  elaborate  Method  for  the 
interpretation  of  Nature.  When  he  protested  against 
the  intellect's  being  left  to  itself  (intellectus  sibi  permissus), 
he  meant  more  than  speculation  left  unchecked  by 
study  of  the  facts.  He  meant  also  that  the  interpreter 
must  have  a  method.  As  man,  he  says,  cannot  move 
rocks  by  the  mere  strength  of  his  hands  without 
instruments,  so  he  cannot  penetrate  to  the  secrets  of 
Nature  by  mere  strength  of  his  intellect  without 
instruments.  These  instruments  he  undertakes  to 
provide  in  his  Inductive  Method  or  Novum  Organum. 
And  it  is  important  to  understand  precisely  what  his 
methods  were,  because  it  is  on  the  ground  of  them  that 
he  is  called  the  founder  of  Inductive  Philosophy,  and 
because  this  has  created  a  misapprehension  of  the 
methods  actually  followed  by  men  of  science. 

Ingenious,  penetrating,  wide-ranging,  happy  in 
nomenclature,  the  Novum  Organum  is  a  wonderful 
monument  of  the  author's  subtle  wit  and  restless 
energy;  but,  beyond  giving  a  general  impulse  to 
testing  speculative  fancies  by  close  comparison  with 
facts,  it  did  nothing  for  science.  His  method — with 
its  Tables  of  Preliminary  Muster  for  the  Intellect 
(tabula  comparenticz  primcz  instantiarum  ad  intellectum, 
facts  collected  and  methodically  arranged  for  the  intel- 
lect to  work  upon) ;  its  Elimination  upon  first  inspection 
of  obviously  accidental  concomitants  (Rejectio  sive 
Exclusiva  naturarum) ;  its  Provisional  Hypothesis 
( Vindemiatio  Prima  sive  Interpretatio  Inchoata) ;  its 
advance  to  a  true  Induction  or  final  Interpretation  by 


Introduction.  249 

examination  of  special  instances  (he  enumerates 
twenty-seven,  3x3x3,  Prerogativas  Instantiarum, 
trying  to  show  the  special  value  of  each  for  the 
inquirer)1 — was  beautifully  regular  and  imposing,  but 
it  was  only  a  vain  show  of  a  method.  It  was  rendered 
so  chiefly  by  the  end  or  aim  that  Bacon  proposed  for 
the  inquirer.  In  this  he  was  not  in  advance  of  his 
age ;  on  the  contrary,  he  was  probably  behind  Roger 
Bacon,  and  certainly  far  behind  such  patient  and 
concentrated  thinkers  as  Copernicus,  Gilbert,  and 
Galileo — no  discredit  to  the  grandeur  of  his  intellect 
when  we  remember  that  science  was  only  his  recreation, 
the  indulgence  of  his  leisure  from  Law  and  State. 

In  effect,  his  method  came  to  this.  Collect  as  many 
instances  as  you  can  of  the  effect  to  be  investigated, 
and  the  absence  of  it  where  you  would  expect  it, 
arrange  them  methodically,  then  put  aside  guesses  at 
the  cause  which  are  obviously  unsuitable,  then  draw 
up  a  probable  explanation,  then  proceed  to  make  this 
exact  by  further  comparison  with  instances.  It  is  when 
we  consider  what  he  directed  the  inquirer  to  search  for 
that  we  see  why  so  orderly  a  method  was  little  likely 
to  be  fruitful. 

He  starts  from  the  principle  that  the  ultimate 
object  of  all  knowledge  is  use,  practice  (sdmus  ut  opert- 
mur).  We  want  to  know  how  Nature  produces  things 
that  we  may  produce  them  for  ourselves,  if  we  can. 
The  inquirer's  first  aim,  therefore,  should  be  to  find 
out  how  the  qualities  of  bodies  are  produced,  to  dis- 
cover the  formes,  or  formal  causes  of  each  quality.  An 


1  The  Novum  Organum  was  never  completed.  Of  the  nine 
heads  of  special  aids  to  the  intellect  in  the  final  interpretation  he 
completed  only  the  first,  the  list  of  Prerogative  Instances. 


250         Indttctive  Logic,  or  the  Logic  of  Science. 

example  shows  what  he  meant  by  this.  Gold  is  a 
crowd  or  conjugation  of  various  qualities  or  "natures"; 
it  is  yellow,  it  has  a  certain  weight,  it  is  malleable  or 
ductile  to  a  certain  degree,  it  is  not  volatile  (loses 
nothing  under  fire),  it  can  be  melted,  it  is  soluble.  If 
we  knew  the  forma  or  formal  cause  of  each  of  those 
qualities,  we  could  make  gold,  provided  the  causes 
were  within  our  control.  The  first  object,  then,  of  the 
investigator  of  Nature  is  to  discover  such  forma,  in 
order  to  be  able  to  effect  the  transformation  of  bodies. 
It  may  be  desirable  also  to  know  the  latens  processus, 
any  steps  not  apparent  to  the  senses  by  which  a  body 
grows  from  its  first  germs  or  rudiments,  and  the 
schematismus  or  ultimate  inner  constitution  of  the  body. 
But  the  discovery  of  the  formes  of  the  constituent 
qualities  (naturcz  singulce),  heat,  colour,  density  or 
rarity,  sweetness,  saltness,  and  so  forth,  is  the  grand 
object  of  the  Interpreter  of  Nature ;  and  it  is  tor  this 
that  Bacon  prescribed  his  method. 

The  Sylva  Sylvarum,  or  Natural  History,  a  miscel- 
laneous collection  of  facts  and  fictions,  observations 
and  traditions,  with  guesses  at  the  explanation  of 
them,  affords  us  a  measure  of  Bacon's  own  advance- 
ment as  an  interpreter  of  Nature.  It  was  a  posthumous 
work,  and  the  editor,  his  secretary,  tells  us  that  he 
often  said  that  if  he  had  considered  his  reputation  he 
would  have  withheld  it  from  the  world,  because  it  was 
not  digested  according  to  his  own  method :  yet  he 
persuaded  himself  that  the  causes  therein  assigned  were 
far  more  certain  than  those  rendered  by  others,  "  not 
for  any  excellence  of  his  own  wit,  but  in  respect  of  his 
continual  conversation  with  Nature  and  Experience," 
and  mankind  might  stay  upon  them  till  true  Axioms 
were  more  fully  discovered.  When,  however,  we 


Introduction.  251 

examine  the  causes  assigned,  we  find  that  in  practice 
Bacon  could  not  carry  out  his  own  precepts  :  that  he 
did  not  attempt  to  creep  up  to  an  explanation  by  slow 
and  patient  ascent,  but  jumped  to  the  highest 
generalisations  :  and  that  his  explanatory  notions  were 
taken  not  from  nature,  but  from  the  ordinary  traditions 
of  mediaeval  physical  science.  He  deceived  himself,  in 
short,  in  thinking  that  he  could  throw  aside  tradition 
and  start  afresh  from  observation. 

For  example.  He  is  struck  by  the  phenomenon  of 
bubbles  on  water  :  "  It  seemeth  somewhat  strange 
that  the  air  should  rise  so  swiftly,  while  it  is  in  the 
water,  and  when  it  cometh  to  the  top  should  be  stayed 
by  so  weak  a  cover  as  that  of  the  bubble  is".  The 
swift  ascent  of  the  air  he  explains  as  a  "  motion  of 
percussion,"  the  water  descending  and  forcing  up  the 
air,  and  not  a  "motion  of  levity"  in  the  air  itself. 
"The  cause  of  the  enclosure  of  the  bubble  is  for  that 
the  appetite  to  resist  separation  or  discontinuance,. 
which  is  strong  in  solids,  is  also  in  liquors,  though 
fainter  and  weaker."  "The  same  reason  is  of  the 
roundness  of  the  bubble,  as  well  for  the  skin  of 
water  as  for  the  air  within.  For  the  air  likewise 
avoideth  discontinuance,  and  therefore  casteth  itself 
into  a  round  figure.  And  for  the  stop  and  arrest  of 
the  air  a  little  while,  it  showeth  that  the  air  of  itself 
hath  little  or  no  appetite  of  ascending."  1  These  notions 
were  not  taken  direct  from  the  facts  :  they  descended 
from  Aristotle.  He  differs  from  Aristotle,  however, 
in  his  explanation  of  the  colours  of  birds'  feathers. 
"  Aristotle  giveth  the  cause  vainly  "  that  birds  are  more 
in  the  beams  of  the  sun  than  beasts.  "  But  that  is 


Sylvarum,  Century  i,  24. 


252         Inductive  Logic,  or  the  Logic  of  Science. 

manifestly  untrue;  for  cattle  are  more  in  the  sun 
than  birds,  that  live  commonly  in  the  woods  or 
in  some  covert.  The  true  cause  is  that  the  excremen- 
titious  moisture  of  living  creatures,  which  maketh  as 
well  the  feathers  in  birds  as  the  hair  in  beasts,  passeth 
in  birds  through  a  finer  and  more  delicate  strainer 
than  it  doth  in  beasts.  For  feathers  pass  through 
quills,  and  hair  through  skin."  It  is  an  instance  of 
percolation  or  filtering :  other  effects  of  the  same  cause 
being  the  gums  of  trees,  which  are  but  a  fine  passage  or 
straining  of  the  juice  through  the  wood  and  bark,  and 
Cornish  Diamonds  and  Rock  Rubies,  which  are  in  like 
manner  "  fine  exudations  of  stone''.1 

These  examples  of  Bacon's  Inductions  are  taken 
from  the  Sylva  at  random.  But  the  example  which 
best  of  all  illustrates  his  attitude  as  a  scientific 
investigator  is  the  remark  he  makes  in  the  Novum 
Organum  about  the  Copernican  theory.  Elsewhere  he 
says  that  there  is  nothing  to  choose  between  it  and  the 
Ptolemaic ;  and  in  the  Novum  Organum  (lib.  ii.  5)  he 
remarks  that  "  no  one  can  hope  to  terminate  the 
question  whether  in  diurnal  motion  it  is  really  the 
earth  or  the  sky  that  rotates,  unless  he  shall  first  have 
comprehended  the  nature  of  spontaneous  rotation". 
That  is,  we  must  first  find  out  the  forma  or  formal 
cause  of  spontaneous  rotation.  This  is  a  veritable 
imtantia  crucis,  as  fixing  Bacon's  place  in  the  mediaeval 
and  not  in  the  new  world  of  scientific  speculation. 

Bacon,  in  short,  in  the  practice  of  induction  did  not 
advance  an  inch  beyond  Aristotle.  Rather  he  retro- 
graded, inasmuch  as  he  failed  to  draw  so  clear  a  line 
between  the  respective  spheres  of  Inductive  collection 

1  Sylva  Sylvarum,  Century  i,  5. 


Introduction.  253 

of  facts  and  Explanation.  There  are  two  sources  of 
general  propositions,  according  to  Aristotle,  Induction 
and  Nous.  By  Induction  he  meant  the  generalisation 
of  facts  open  to  sense,  the  summation  of  observed 
particulars,  the  inductio  per  enumerationem  simplicem  of 
the  schoolmen.  By  Nous  he  meant  the  Reason  or 
Speculative  Faculty,  as  exercised  with  trained  sagacity 
by  experts.  Thus  by  Induction  we  gather  that  all 
homed  animals  ruminate.  The  explanation  of  this 
is  furnished  by  the  Nous,  and  the  explanation  that 
commended  itself  to  the  trained  sagacity  of  his  time 
was  that  Nature  having  but  a  limited  amount  of  hard 
material  and  having  spent  this  on  the  horns,  had  none 
left  for  teeth,  and  so  provided  four  stomachs  by  way  of 
compensation.  Bacon's  guesses  at  causes  are  on  the 
same  scientific  level  with  this,  only  he  rather  confused 
matters  by  speaking  of  them  as  if  they  were  inductions 
from  fact,  instead  of  being  merely  fancies  superinduced 
upon  fact.  His  theory  of  interpretation,  it  is  true,  was 
so  far  an  advance  that  he  insisted  on  the  necessity  of 
verifying  every  hypothesis  by  further  appeal  to  facts, 
though  in  practice  he  himself  exercised  no  such 
patience  and  never  realised  the  conditions  of  verification. 
Against  this,  again,  must  be  set  the  fact  that  by  calling 
his  method  induction,  and  laying  so  much  stress  on 
the  collection  of  facts,  he  fostered,  and,  indeed,  fixed 
in  the  public  mind  the  erroneous  idea  that  the  whole 
work  of  science  consists  in  observation.  The  goal  of 
science,  as  Herschel  said,  is  Explanation,  though 
every  explanation  must  be  made  to  conform  to  fact, 
and  explanation  is  only  another  term  for  attaining  to 
higher  generalisations,  higher  unities. 

The  truth  is  that  Induction,  if  that  is  the  name  we 
use  for  scientific  method,  is  not,  as  Reid  conceived,  an 


254         Inductive  Logic ,  or  the  Logic  of  Science. 

exception  to  the  usual  rule  of  arts  in  being  the  invention 
of  one  man.  Bacon  neither  invented  nor  practised  it. 
It  was  perfected  gradually  in  the  practice  of  men  of 
science.  The  birthplace  of  it  as  a  conscious  method 
was  in  the  discussions  of  the  Royal  Society  of  London, 
as  the  birthplace  of  the  Aristotelian  Logic  was  in  the 
discussions  of  the  Athenian  schools.  Its  first  great 
triumph  was  Newton's  law  of  Gravitation.  If  we  are 
to  name  it  after  its  first  illustrious  practitioner,  we 
must  call  it  the  Newtonian  method,  not  the  Baconian. 
Newton  really  stands  to  the  Scientific  Method  of 
Explanation  as  Aristotle  stands  to  the  Method  of 
Dialectic  and  Deduction.  He  partly  made  it  explicit 
in  his  Regulce.  Philosophandi  (1685).  Locke,  his  friend 
and  fellow-member  of  the  Royal  Society,  who  applied 
the  method  to  the  facts  of  Mind  in  his  Essay  Concerning 
Human  Understanding  (1691),  made  it  still  further 
explicit  in  the  Fourth  Book  of  that  famous  work. 

It  was,  however,  a  century  and  a  half  later  that  an 
attempt  was  first  made  to  incorporate  scientific  method 
with  Logic  under  the  name  of  Induction,  and  add  it  as 
a  new  wing  to  the  old  Aristotelian  building.  This  was 
the  work  of  John  Stuart  Mill,  whose  System  of  Logic, 
Deductive  and  Inductive,  was  first  published  in  1843. 

The  genesis  of  Mill's  System  of  Logic,  as  of  other 
things,  throws  light  upon  its  character.  And  in 
inquiries  into  the  genesis  of  anything  that  man  makes 
we  may  profitably  follow  Aristotle's  division  of  causes. 
The  Efficient  Cause  is  the  man  himself,  but  we  have 
also  to  find  out  the  Final  Cause,  his  object  or  purpose 
in  making  the  thing,  the  Material  Cause,  the  sources 
of  his  material,  and  the  Formal  Cause,  the  reason  why 
he  shaped  it  as  he  did.  In  the  case  of  Mill's  system 
we  have  to  ask :  What  first  moved  him  to  formulate 


Introduction .  255 

the  methods  of  scientific  investigation  ?  Whence  did 
he  derive  his  materials  ?  Why  did  he  give  his  scientific 
method  the  form  of  a  supplement  to  the  old  Aristotelian 
Logic  ?  We  cannot  absolutely  separate  the  three 
inquiries,  but  motive,  matter  and  form  each  had  a 
traceable  influence  on  the  leading  features  of  his 
System. 

First,  then,  as  to  his  motive.  It  is  a  mistake  to 
suppose  that  Mill's  object  was  to  frame  an  organon 
that  might  assist  men  of  science  as  ordinarily  under- 
stood in  making  discoveries.  Bacon,  his  secretary 
tells  us,  was  wont  to  complain  that  he  should  be 
forced  to  be  a  Workman  and  a  Labourer  in  science 
when  he  thought  he  deserved  to  be  an  Architect  in  this 
building.  And  men  of  science  have  sometimes  rebuked 
Mill  for  his  presumption  in  that,  not  being  himself  an 
investigator  in  any  department  of  exact  science,  he  should 
volunteer  to  teach  them  their  business.  But  Mill  was 
really  guilty  of  no  such  presumption.  His  object,  on 
the  contrary,  was  to  learn  their  method  with  a  view  to 
its  application  to  subjects  that  had  not  yet  undergone 
scientific  treatment.  Briefly  stated,  his  purpose 
was  to  go  to  the  practical  workers  in  the  exact 
sciences,  Astronomy,  Chemistry,  Heat,  Light,  Elec- 
tricity, Molar  and  Molecular  Physics;  ascertain, 
not  so  much  how  they  made  their  discoveries  as 
how  they  assured  themselves  and  others  that  their 
conclusions  were  sound  ;  and  having  ascertained  their 
tests  of  truth  and  principles  of  proof,  to  formulate  these 
tests  so  that  they  might  be  applied  to  propositions 
outside  the  range  of  the  exact  sciences,  propositions  in 
Politics,  Ethics,  History,  Psychology.  More  particu- 
larly he  studied  how  scientific  men  verify,  and  when 
they  accept  as  proved,  propositions  of  causation,  expla- 


256         Inductive  Logic,  or  the  Logic  of  Science. 

nations  of  the  causes  of  things.  In  effect,  his  survey 
of  scientific  method  was  designed  to  lead  up  to  the 
Sixth  Book  in  his  System,  the  Logic  of  the  Moral 
Sciences.  There  are  multitudes  of  floating  endoxes 
or  current  opinions  concerning  man  and  his  concerns, 
assigning  causes  for  the  conduct  and  character  of 
individuals  and  of  communities.  Mill  showed  himself 
quite  aware  that  the  same  modes  of  investigation  may 
not  be  practicable,  and  that  it  may  not  be  possible, 
though  men  are  always  ready  to  assign  causes  with 
confidence,  to  ascertain  causes  with  the  same  degree 
of  certainty  :  but  at  least  the  conditions  of  exact  verifi- 
cation should  be  the  same,  and  it  is  necessary  to  see 
what  they  are  in  order  to  see  how  far  they  can  be 
realised. 

That  such  was  Mill's  design  in  the  main  is  apparent 
on  internal  evidence,  and  it  was  the  internal  evidence 
that  first  struck  me.  But  there  is  external  evidence  as 
well.  We  may  first  adduce  some  essays  on  the  Spirit 
of  the  Age,  published  in  the  Examiner  in  1831,  essays 
which  drew  from  Carlyle  the  exclamation,  "  Here  is  a 
new  Mystic !  "  These  essays  have  never  been  repub- 
lished,  but  they  contain  Mill's  first  public  expression 
of  the  need  for  a  method  in  social  inquiries.  He  starts 
from  the  Platonic  idea  that  no  state  can  be  stable  in 
which  the  judgment  of  the  wisest  in  political  affairs  is 
not  supreme.  He  foresees  danger  in  the  prevalent 
anarchy  of  opinion.  How  is  it  to  be  averted  ?  How 
are  men  to  be  brought  to  accept  loyally  the  judgment 
of  the  expert  in  public  affairs  ?  They  accept  at  once 
and  without  question  the  decisions  of  the  specially 
skilled  in  the  physical  sciences.  Why  is  this  ?  For 
one  reason,  because  there  is  complete  agreement 
among  experts.  And  why  is  there  this  complete 


Introduction .  257 

agreement  ?  Because  all  accept  the  same  tests  of 
truth,  the  same  conditions  of  proof.  Is  it  not  possible 
to  obtain  among  political  investigators  similar 
unanimity  as  to  their  methods  of  arriving  at  con- 
clusions, so  as  to  secure  similar  respect  for  their 
authority  ? 

We  need  not  stop  to  ask  whether  this  was  a  vain 
dream,  and  whether  it  must  not  always  be  the  case 
that  to  ensure  confidence  in  a  political  or  moral 
adviser  more  is  needed  than  faith  in  his  special  know- 
ledge and  trained  sagacity.  Our  point  is  that  in 
1831  Mill  was  in  search  of  a  method  of  reasoning  in 
social  questions.  Opportunely  soon  after,  early  in 
1832,  was  published  Herschel's  Discourse  on  the  Study 
of  Natural  Philosophy,  the  first  attempt  by  an  eminent 
man  -of  science  to  make  the  methods  of  science 
explicit.  Mill  reviewed  this  book  in  the  Examiner, 
and  there  returns  more  definitely  to  the  quest  on  which 
he  was  bent.  "The  uncertainty,"  he  says,  "that 
hangs  over  the  very  elements  of  moral  and  social 
philosophy  proves  that  the  means  of  arriving  at  the 
truth  in  those  sciences  are  not  yet  properly  understood. 
And  whither  can  mankind  so  advantageously  turn,  in 
order  to  learn  the  proper  means  and  to  form  their 
minds  to  the  proper  habits,  as  to  that  branch  of  know- 
ledge in  which  by  universal  acknowledgment  the 
greatest  number  of  truths  have  been  ascertained  and 
the  greatest  possible  degree  of  certainty  arrived  at  ?  " 

We  learn  from  Mill  himself  that  he  made  an  attempt 
about  this  time,  while  his  mind  was  full  of  Herschel's 
Discourse,  to  connect  a  scientific  method  with  the 
body  of  the  Old  Logic.  But  he  could  not  make  the 
junction  to  his  satisfaction,  and  abandoned  the  attempt 
in  despair.  A  little  later,  in  1837,  upon  the  appearance 


258         Inductive  Logic,  or  the  Logic  of  Science. 

of  Whewell's  History  of  the  Inductive  Sciences,  he 
renewed  it,  and  this  time  with  happier  results. 
Whewell's  Philosophy  of  the  Inductive  Sciences  was 
published  in  1840,  but  by  that  time  Mill's  system  was 
definitely  shaped. 

It  was,  then,  to  Herschel  and  Whewell,  but 
especially  to  the  former,  that  Mill  owed  the  raw  materials 
of  his  Inductive  Method.  But  why  did  he  desire  to 
concatenate  this  with  the  old  Logic  ?  Probably 
because  he  considered  that  this  also  had  its  uses  for 
the  student  of  society,  the  political  thinker.  He  had 
inherited  a  respect  for  the  old  Logic  from  his  father. 
But  it  was  the  point  at  which  he  sought  to  connect  the 
new  material  with  the  old,  the  point  of  junction 
between  the  two,  that  determined  the  form  of  his 
system.  We  find  the  explanation  of  this  in  the  history 
of  the  old  Logic.  It  so  happened  that  Whately's 
Logic  was  in  the  ascendant,  and  Whately's  treatment 
of  Induction  gives  the  key  to  Mill's. 

Towards  the  end  of  the  first  quarter  of  this  century 
there  was  a  great  revival  of  the  study  of  Logic  at 
Oxford.  The  study  had  become  mechanical,  Aldrich's 
Compendium,  an  intelligent  but  exceedingly  brief 
abstract  of  the  Scholastic  Logic,  being  the  text-book 
beyond  which  no  tutor  cared  to  go.  The  man  who 
seems  to  have  given  new  life  to  the  study  was  a  tutor 
who  subsequently  became  Bishop  of  Llandaff,  Edward 
Copleston.  The  first  public  fruits  of  the  revival  begun 
by  him  was  Whately's  article  on  Logic  in  the  Encyclo- 
pedia Metropolitan ,  published  as  a  separate  book  in 
1827.  Curiously  enough,  one  of  Whately's  most 
active  collaborators  in  the  work  was  John  Henry 
Newman,  so  that  the  common  room  of  Oriel,  which 
Mr.  Froude  describes  as  the  centre  from  which 


Introduction.  259 

emanated  the  High  Church  Movement,  may  also  be 
said  to  have  been  the  centre  from  which  emanated  the 
movement  that  culminated  in  the  revolution  of  Logic. 

The  publication  of  Whately's  Logic  made  a  great  stir. 
It  was  reviewed  by  Mill,  then  a  young  man  of  twenty-one, 
in  the  Westminster  Review  (1828),  and  by  Hamilton,  then 
forty-five  years  of  age,  in  the  Edinburgh  (1833).  There 
can  be  no  doubt  that  it  awakened  Mill's  interest  in  the 
subject.  A  society  formed  for  the  discussion  of  philo- 
sophical questions,  and  called  the  Speculative  Society, 
met  at  Grote's  house  in  1825,  and  for  some  years 
following.  Of  this  society  young  Mill  was  a  member, 
and  their  continuous  topic  in  1827  was  Logic,  Whately's 
treatise  being  used  as  a  sort  of  text-book. 

It  is  remarkable  that  Mill's  review  of  Whately,  the 
outcome  of  these  discussions,  says  very  little  about 
Induction.  At  that  stage  Mill's  chief  concern  seems 
to  have  been  to  uphold  the  usefulness  of  Deductive 
Logic,  and  he  even  goes  so  far  as  to  scoff  at  its 
eighteenth  century  detractors  and  their  ambition  to 
supersede  it  with  a  system  of  Induction.  The  most 
striking  feature  of  the  article  is  the  brilliant  defence  of 
the  Syllogism  as  an  analysis  of  arguments  to  which  I 
have  already  referred.  He  does  not  deny  that  an 
Inductive  Logic  might  be  useful  as  a  supplement,  but 
apparently  he  had  not  then  formed  the  design  of  supply- 
ing such  a  supplement.  When,  however,  that  design 
seriously  entered  his  mind,  consequent  upon  the  felt  need 
of  a  method  for  social  investigations,  it  was  Whately's 
conception  of  Induction  that  he  fell  back  upon.  His- 
torically viewed,  his  System  of  Logic  was  an  attempt 
to  connect  the  practical  conditions  of  proof  set  forth  in 
Herschel's  discourse  with  the  theoretic  view  of  Induc- 
tion propounded  in  Whately's.  The  tag  by  which  he 


260         Inductive  Logic,  or  the  Logic  of  Science. 

sought  to  attach  the  new  material  to  the  old  system 
was  the  Inductive  Enthymeme  of  the  Schoolmen  as 
interpreted  by  Whately. 

Whately's  interpretation — or  misinterpretation — of 
this  Enthymeme,  and  the  conception  of  Induction 
underlying  it,  since  it  became  Mill's  ruling  conception 
of  Induction,  and  virtually  the  formative  principle  of 
his  system,  deserves  particular  attention. 

"This,  that  and  the  other  horned  animal,  ox,  sheep, 
goat,  ruminate;  therefore,  all  horned  animals  ruminate." 

The  traditional  view  of  this  Enthymeme  I  have  given 
in  my  chapter  on  Formal  Induction  (p.  238).  It  is 
that  a  Minor  Premiss  is  suppressed  :  "  This,  that 
and  the  other  constitute  the  whole  class".  This  is 
the  form  of  the  Minor  in  Aristotle's  Inductive  Syllo- 
gism. 

But,  Whately  argued,  how  do  we  know  that  this, 
that  and  the  other — the  individuals  we  have  examined 
— constitute  the  whole  class  ?  Do  we  not  assume  that 
what  belongs  to  the  individuals  examined  belongs  to 
the  whole  class  ?  This  tacit  assumption,  he  contended, 
is  really  at  the  bottom  of  the  Enthymeme,  and  its 
proper  completion  is  to  take  this  as  the  Major  Premiss, 
with  the  enumeration  of  individuals  as  the  Minor. 
Thus  :— 

What  belongs  to  the  individuals  examined  belongs  to 

the  whole  class. 
The  property  of  ruminating  belongs  to  the  individuals 

examined,  ox,  sheep,  goat,  etc. 
Therefore,  it  belongs  to  all. 

In  answer  to  this,  Hamilton  repeated  the  traditional 
view,  treating  Whately's  view  merely  as  an  instance  of 


Introduction.  261 

the  prevailing  ignorance  of  the  history  of  Logic.  He 
pointed  out  besides  that  Whately's  Major  was  the 
postulate  of  a  different  kind  of  inference  from  that 
contemplated  in  Aristotle's  Inductive  Syllogism, 
Material  as  distinguished  from  Formal  inference, 
This  is  undeniable  if  we  take  this  syllogism  purely  as 
an  argumentative  syllogism  The  "all"  of  the  con 
elusion  simply  covers  the  individuals  enumerated  and 
admitted  to  be  "  all "  in  the  Minor  Premiss.  If  a 
disputant  admits  the  cases  produced  to  be  all  and  can 
produce  none  to  the  contrary,  he  is  bound  to  admit 
the  conclusion.  Now  the  inference  contemplated  by 
Whately  was  not  inference  from  an  admission  to  what 
it  implies,  but  inference  from  a  series  of  observations 
to  all  of  a  like  kind,  observed  and  unobserved. 

It  is  not  worth  while  discussing  what  historical 
justification  Whately  had  for  his  view  of  Induction. 
It  is  at  least  arguable  that  the  word  had  come  to  mean, 
if  it  did  not  mean  with  Aristotle  himself,  more  than  a 
mere  summation  of  particulars  in  a  general  statement. 
Even  Aristotle's  respondent  in  the  concession  of  his 
Minor  admitted  that  the  individuals  enumerated  con- 
stituted all  in  the  truly  general  sense,  not  merely  all 
observed  but  all  beyond  the  range  of  observation.  The 
point,  however,  is  insignificant.  What  really  signifies 
is  that  while  Hamilton,  after  drawing  the  line  between 
Formal  Induction  and  Material,  fell  back  and  entrenched 
himself  within  that  line,  Mill  caught  up  Whately's 
conception  of  Induction,  pushed  forward,  and  made  it 
the  basis  of  his  System  of  Logic. 

In  Mill's  definition,  the  mere  summation  of  particu- 
lars, Inductio  per  enumerationem  simplicem  ubi  non 
reperitur  instantia  contradictoria^  is  Induction  improperly 
so  called.  The  only  process  worthy  of  the  name  is 


262         Inductive  Logic,  or  the  Logic  of  Science. 

Material  Induction,  inference  to  the  unobserved.  Here 
only  is  there  an  advance  from  the  known  to  the 
unknown,  a  veritable  **  inductive  hazard  ". 

Starting  then  with  this  conception  of  inference  to 
the  unobserved  as  the  only  true  inference,  and  with  an 
empirical  law — a  generality  extended  from  observed 
cases  to  unobserved — as  the  type  of  such  inference, 
Mill  saw  his  way  to  connecting  a  new  Logic  with  the 
old.  We  must  examine  this  junction  carefully,  and 
the  brilliant  and  plausible  arguments  by  which  he 
supported  it ;  we  shall  find  that,  biased  by  this  desire 
to  connect  the  new  with  the  old,  he  gave  a  misleading 
dialectic  setting  to  his  propositions,  and,  in  effect, 
confused  the  principles  of  Argumentative  conclusion 
on  the  one  hand  and  of  Scientific  Observation  and 
Inference  on  the  other.  The  conception  of  Inference 
which  he  adopted  from  Whately  was  too  narrow  on 
both  sides  for  the  uses  to  which  he  put  it.  Be  it 
understood  that  in  the  central  methods  both  of  Syllo- 
gistic and  of  Science,  Mill  was  substantially  in  accord 
with  tradition ;  it  is  in  his  mode  of  junction,  and  the 
light  thereby  thrown  upon  the  ends  and  aims  of  both, 
that  he  is  most  open  to  criticism. 

As  regards  the  relation  between  Deduction  and 
Induction,  Mill's  chief  proposition  was  the  brilliant 
paradox  that  all  inference  is  at  bottom  Inductive,  that 
Deduction  is  only  a  partial  and  accidental  stage  in  a 
process  the  whole  of  which  may  be  called  Induction. 
An  opinion  was  abroad— fostered  by  the  apparently 
exclusive  devotion  of  Logic  to  Deduction— that  all 
inference  is  essentially  Deductive.  Not  so,  answered 
Mill,  meeting  this  extreme  with  another  :  all  inference 
is  essentially  Inductive.  He  arrives  at  this  through 
the  conception  that  Induction  is  a  generalisation  from 


Introduction.  263 

observed  particulars,  while  Deduction  is  merely  the 
extension  of  the  generalisation  to  a  new  case,  a  new 
particular.  The  example  that  he  used  will  make  his 
meaning  plain. 

Take  a  common  Syllogism  : — 

All  men  are  mortal. 
Socrates  is  a  man. 
Socrates  is  mortal. 

"  The  proposition,"  Mill  says,  "  that  Socrates  is  mortal 
is  evidently  an  inference.  It  is  got  at  as  a  conclusion 
from  something  else.  But  do  we  in  reality  conclude 
it  from  the  proposition,  All  men  are  mortal?"-  He 
answers  that  this  cannot  be,  because  if  it  is  not  true  that 
Socrates  is  mortal  it  cannot  be  true  that  all  men'  are 
mortal.  It  is  clear  that  our  belief  in  the  mortality  of 
Socrates  must  rest  on  the  same  ground  as  our  belief 
in  the  mortality  of  men  in  general.  He  goes  on  to 
ask  whence  we  derive  our  knowledge  of  the  general 
truth,  and  answers :  "  Of  course  from  observation. 
Now  all  which  man  can  observe  are  individual  cases. 
...  A  general  truth  is  but  an  aggregate  of  particular 
truths.  But  a  general  proposition  is  not  merely  a 
compendious  form  for  recording  a  number  of  particular 
facts.  ...  It  is  also  a  process  of  inference.  From 
instances  which  we  have  observed  we  feel  warranted 
in  concluding  that  what  we  have  found  true  in  those 
instances,  holds  in  all  similar  ones,  past,  present,  and 
future.  We  then  record  all  that  we  have  observed 
together  with  what  we  infer  from  our  observations,  in 
one  concise  expression."  A  general  proposition  is 
thus  at  once  a  summary  of  particular  facts  and  a 
memorandum  of  our  right  to  infer  from  them.  And 
when  we  make  a  deduction  we  are,  as  it  were, 


264         Inductive  Logic,  or  the  Logic  of  Science. 

interpreting  this  memorandum.  But  it  is  upon  the 
particular  facts  that  the  inference  really  rests,  and  Mill 
contends  that  we  might  if  we  chose  infer  to  the 
particular  conclusion  at  once  without  going  through 
the  form  of  a  general  inference.  Thus  Mill  seeks  to 
make  good  his  point  that  all  inference  is  essentially 
Inductive,  and  that  it  is  only  for  convenience  that  the 
word  Induction  has  been  confined  to  the  general 
induction,  while  the  word  Deduction  is  applied  to  the 
process  of  interpreting  our  memorandum. 

Clear  and  consecutive  as  this  argument  is,  it  is 
fundamentally  confusing.  It  confuses  the  nature 
of  Syllogistic  conclusion  or  Deduction,  and  at  the 
same  time  gives  a  partial  and  incomplete  account  of 
the  ground  of  Material  inference. 

The  root  of  the  first  confusion  lies  in  raising  the 
question  of  the  ground  of  material  inference  in  con- 
nexion with  the  Syllogism.  As  regards  the  usefulness 
of  the  Syllogism,  this  is  an  IGNORATIO  ELENCHI.  That 
the  Major  and  the  conclusion  rest  upon  the  same  ground 
as  matters  of  belief  is  indisputable  :  but  it  is  irrelevant. 
In  so  far  as  "  Socrates  is  mortal "  is  an  inference  from 
facts,  it  is  not  the  conclusion  of  a  Syllogism.  This  is 
implicitly  and  with  unconscious  inconsistency  recog- 
nised by  Mill  when  he  represents  Deduction  as  the 
interpretation  of  a  memorandum.  To  represent 
Deduction  as  the  interpretation  of  a  memorandum — a 
very  happy  way  of  putting  it  and  quite  in  accordance 
with  Roger  Bacon's  view — is  really  inconsistent  with 
regarding  Deduction  as  an  occasional  step  in  the 
process  of  Induction.  If  Deduction  is  the  interpretation 
of  a  memorandum,  it  is  no  part  of  the  process  of 
inference  from  facts.  The  conditions  of  correct 
interpretation  as  laid  down  in  Syllogism  are  one  thing, 


Introduction.  265 

and  the  methods  of  correct  inference  from  facts,  the 
methods  of  science  that  he  was  in  search  of,  are 
another. 

Let  us  emphasise  this  view  of  Deduction  as  the 
interpretation  of  a  memorandum.  It  corresponds 
exactly  with  the  view  that  I  have  taken  in  discussing 
the  utility  of  the  Syllogism.  Suppose  we  want  to 
know  whether  a  particular  conclusion  is  consistent 
with  our  memorandum,  what  have  we  to  look  to  ?  We 
have  to  put  our  memorandum  into  such  a  form  that  it 
is  at  once  apparent  whether  or  not  it  covers  our 
particular  case.  The  Syllogism  aspires  to  be  such  a 
form.  That  is  the  end  r.nd  aim  of  it.  It  does  not 
enable  us  to  judge  whether  the  memorandum  is  a 
legitimate  memorandum  or  not.  It  only  makes  clear 
that  if  the  memorandum  is  legitimate,  so  is  the  con- 
clusion. How  to  make  clear  and  consistent  memoranda 
of  our  beliefs  in  words  is  a  sufficiently  complete  de- 
scription of  the  main  purpose  of  Deductive  Logic. 

Instead,  then,  of  trying  to  present  Deduction  and 
Induction  as  parts  of  the  same  process,  which  he  was 
led  to  do  by  his  desire  to  connect  the  new  and  the  old, 
Mill  ought  rather,  in  consistency  as  well  as  in  the 
interests  of  clear  system,  to  have  drawn  a  line  of 
separation  between  the  two  as  having  really  different 
ends,  the  conditions  of  correct  conclusion  from  accepted 
generalities  on  the  one  hand,  and  the  conditions  of 
correct  inference  from  facts  on  the  other.  Whether  the 
first  should  be  called  inference  at  all  is  a  question  of 
naming  that  ought  to  have  been  considered  by  itself. 
We  may  refuse  to  call  it  inference,  but  we  only  confuse 
ourselves  and  others  if  we  do  not  acknowledge  that 
in  so  doing  we  are  breaking  with  traditional  usage. 
Perhaps  the  best  way  in  the  interests  of  clearness  is  to 


266         Inductive  Logic,  or  the  Logic  of  Science. 

compromise  with  tradition  by  calling  the  one  Formal 
Inference  and  the  other  Material  Inference. 

It  is  with  the  latter  that  the  Physical  Sciences  are 
mainly  concerned,  and  it  was  the  conditions  and 
methods  of  its  correct  performance  that  Mill  desired  to 
systematise  in  his  Inductive  Logic.  We  have  next  to 
see  how  his  statement  of  the  grounds  of  Material 
Inference  was  affected  by  his  connexion  of  Deduction 
and  Induction.  Here  also  we  shall  find  a  reason  for  a 
clearer  separation  between  the  two  departments  of 
Logic. 

In  his  antagonism  to  a  supposed  doctrine  that  all 
reasoning  is  from  general  to  particular,  Mill  maintained 
simpliciter  that  all  reasoning  is  from  particulars  to 
particulars.  Now  this  is  true  only  secundum  quid,  and 
although  in  the  course  of  his  argument  Mill  introduced 
the  necessary  qualifications,  the  unqualified  thesis  was 
confusing.  It  is  perfectly  true  that  we  may  infer — we 
can  hardly  be  said  to  reason — from  observed  particulars 
to  unobserved.  We  may  even  infer,  and  infer  correctly, 
from  a  single  case.  The  village  matron,  called  in  to 
prescribe  for  a  neighbour's  sick  child,  infers  that  what 
cured  her  own  child  will  cure  the  neighbour's,  and 
prescribes  accordingly.  And  she  may  be  right.  But 
it  is  also  true  that  she  may  be  wrong,  and  that  no 
fallacy  is  more  common  than  reasoning  from  particulars 
to  particulars  without  the  requisite  precautions.  This 
is  the  moral  of  one  of  the  fables  of  Camerarius.  Two 
donkeys  were  travelling  in  the  same  caravan,  the  one 
laden  with  salt,  the  other  with  hay.  The  one  laden  with 
salt  stumbled  in  crossing  a  stream,  his  panniers  dipped 
in  the  stream,  the  salt  melted,  and  his  burden  was 
lightened.  When  they  came  to  another  stream,  the 
donkey  that  was  laden  with  hay  dipped  his  panniers 


Introduction,  267 

in  the  water,  expecting  a  similar  result.  Mill's  illustra- 
tions of  correct  inference  from  particulars  to  particulars 
were  really  irrelevant.  What  we  are  concerned  with  in 
considering  the  grounds  of  Inference,  is  the  condition 
of  correct  inference,  and  no  inference  to  an  unobserved 
case  is  sound  unless  it  is  of  a  like  kind  with  the 
observed  case  or  cases  on  which  it  is  founded,  that 
is  to  say,  unless  we  are  entitled  to  make  a  general 
proposition.  We  need  not  go  through  the  form  of 
making  a  general  proposition,  but  if  a  general  proposi- 
tion for  all  particulars  of  a  certain  description  is  not 
legitimate,  no  more  is  the  particular  inference.  Mill, 
of  course,  did  not  deny  this,  he  was  only  betrayed  by 
the  turn  of  his  polemic  into  an  unqualified  form  of 
statement  that  seemed  to  ignore  it. 

But  this  was  not  the  worst  defect  of  Mill's  attempt 
at  a  junction  of  old  and  new  through  Whately's  con- 
ception of  Induction.  A  more  serious  defect  was  due 
to  the  insufficiency  of  this  conception  to  represent  all 
the  modes  of  scientific  inference.  When  a  certain 
attribute  has  been  found  in  a  certain  connexion  in  this, 
that,  and  the  other,  to  the  extent  of  all  observed 
instances,  we  infer  that  it  will  be  found  in  all,  that  the 
connexion  that  has  obtained  within  the  range  of  our 
actual  experience  has  obtained  beyond  that  range  and 
will  obtain  in  the  future.  Call  this  an  observed  uni- 
formity of  nature :  we  hold  ourselves  justified  in 
expecting  that  the  observed  uniformities  of  nature  will 
continue.  Such  an  observed  uniformity — that  All 
animals  have  a  nervous  system,  that  All  animals  die, 
that  Quinine  cures  ague — is  also  called  an  Empirical 
Law. 

But  while  we  are  justified  in  extending  an  empirical 
law  beyond  the  limits  within  which  it  has  been 


268         Inductive  Logic,  or  the  Logic  of  Science. 

observed  to  hold  good,  it  is  a  mistake  to  suppose  that 
the  main  work  of  science  is  the  collection  of  empirical 
laws,  and  that  the  only  scientific  inference  is  the 
inference  from  the  observed  prevalence  of  an  empirical 
law  to  its  continuance.  With  science  the  collection  of 
empirical  laws  is  only  a  preliminary :  "  the  goal  of 
science,"  in  Herschel's  phrase,  "  is  explanation  ".  In 
giving  such  prominence  to  empirical  laws  in  his  theory, 
Mill  confined  Induction  to  a  narrower  scope  than 
science  ascribes  to  it.  Science  aims  at  reaching  "  the 
causes  of  things  "  :  it  tries  to  penetrate  behind  observed 
uniformities  to  the  explanation  of  them.  In  fact,  as  long 
as  a  science  consists  only  of  observed  uniformities,  as 
long  as  it  is  in  the  empirical  stage,  it  is  a  science  only 
by  courtesy.  Astronomy  was  in  this  stage  before  the 
discovery  of  the  Law  of  Gravitation.  Medicine  is 
merely  empirical  as  long  as  its  practice  rests  upon  such 
generalisations  as  that  Quinine  cures  ague,  without 
knowing  why.  It  is  true  that  this  explanation  may 
consist  only  in  the  discovery  of  a  higher  or  deeper  uni- 
formity, a  more  recondite  law  of  connexion  :  the  point 
is  that  these  deeper  laws  are  not  always  open  to 
observation,  and  that  the  method  of  reaching  them  is 
not  merely  observing  and  recording. 

In  the  body  of  his  Inductive  Logic,  Mill  gave  a 
sufficient  account  of  the  Method  of  Explanation 
as  practised  in  scientific  inquiry.  It  was  only  his 
mode  of  approaching  the  subject  that  was  confusing, 
and  made  it  appear  as  if  the  proper  work  of  science 
were  merely  extending  observed  generalities,  as  when 
we  conclude  that  all  men  will  die  because  all  men  have 
died,  or  that  all  horned  animals  ruminate  because  all 
hitherto  observed  have  had  this  attribute.  A  minor 
source  of  confusion  incident  to  the  same  controversy 


Introduction .  269 

was  his  refusing  the  title  of  Induction  proper  to  a  mere 
summary  of  particulars.  He  seemed  thereby  to  cast 
a  slight  upon  the  mere  summation  of  particulars. 
And  yet,  according  to  his  theory,  it  was  those 
particulars  that  were  the  basis  of  the  Induction 
properly  so  called.  That  all  men  will  die  is  an 
inference  from  the  observation  summed  up  in  the 
proposition  that  all  men  have  died.  If  we  refuse 
the  name  of  Induction  to  the  general  proposition  of 
fact,  what  are  we  to  call  it  ?  The  truth  is  that  the 
reason  why  the  word  Induction  is  applied  indifferently 
to  the  general  proposition  of  fact  and  the  general  pro- 
position applicable  to  all  time  is  that,  once  we  are  sure 
of  the  facts,  the  transition  to  the  inference  is  so  simple 
an  affair  that  it  has  not  been  found  necessary  in 
practice  to  distinguish  them  by  different  names. 

Our  criticism  of  Mill  would  itself  mislead  if  it  were 
taken  to  mean  that  the  methods  of  science  which  he 
formulated  are  not  the  methods  of  science  or  that  his 
system  of  those  methods  is  substantially  incomplete. 
His  Inductive  Logic  as  a  system  of  scientific  method 
was  a  great  achievement  in  organisation,  a  veritable 
Novum  Organum  of  knowledge.  What  kept  him  sub- 
stantially right  was  that  the  methods  which  he 
systematised  were  taken  from  the  practice  of  men  of 
science.  Our  criticism  amounts  only  to  this,  that  in 
correlating  the  new  system  with  the  old  he  went  upon 
a  wrong  track.  For  more  than  two  centuries  Deduction 
had  been  opposed  to  Induction,  the  ars  disserendi  to  the 
ars  inveniendi.  In  trying  to  reconcile  them  and  bring 
them  under  one  roof,  Mill  drew  the  bonds  too  tight. 
In  stating  the  terms  of  the  union  between  the  two 
partners,  he  did  not  separate  their  spheres  of  work 
with  sufficient  distinctness. 


270         Inductive  Logic,  or  the  Logic  of  Science. 

Mill's  theory  of  Deduction  and  Induction  and  the 
voluminous  criticism  to  which  in  its  turn  it  has  been 
subjected  have  undoubtedly  been  of  great  service  in 
clearing  up  the  foundations  of  reasoning.  But  the 
moral  of  it  is  that  if  we  are  to  make  the  methods  of 
Science  a  part  of  Logic,  and  to  name  this  department 
Induction,  it  is  better  to  discard  altogether  the  ques- 
tions of  General  and  Particular  which  are  pertinent 
to  Syllogism,  and  to  recognise  the  new  department 
simply  as  being  concerned  with  a  different  kind  of 
inference,  inference  from  facts  to  what  lies  beyond 
them,  inference  from  the  observed  to  the  unobserved. 

That  this  is  the  general  aim  and  proper  work  of 
Science  is  evident  from  its  history.  Get  at  the  secrets 
of  Nature  by  the  study  of  Nature,  penetrate  to  what 
is  unknown  and  unexperienced  by  help  of  what  is 
known  and  has  been  experienced,  was  the  cry  of  the 
early  reformers  of  Science.  Thus  only,  in  Roger 
Bacon's  phrase,  could  certainty — assured,  well  grounded, 
rational  belief — be  reached.  This  doctrine,  like  every 
other,  can  be  understood  only  by  what  it  was  intended 
to  deny.  The  way  of  reaching  certainty  that  Roger 
Bacon  repudiated  was  argument,  discussion,  dialectic. 
This  "  concludes  a  question  but  does  not  make  us  feel 
certain,  or  acquiesce  in  the  contemplation  of  truth  that 
is  not  also  found  in  Experience".  Argument  is  not 
necessarily  useless ;  the  proposition  combated  is  only 
that  by  it  alone — by  discussion  that  does  not  go  beyond 
accepted  theories  or  conceptions— rational  belief  about 
the  unknown  cannot  be  reached.  The  proposition 
affirmed  is  that  to  this  end  the  conclusions  of  argument 
must  be  tested  by  experience. 

Observation  of  facts  then  is  a  cardinal  part  of  the 
method  of  Science.  The  facts  on  which  our  inferences 


Introduction.  271 

are  based,  by  which  our  conclusions  are  tested,  must 
be  accurate.  But  in  thus  laying  emphasis  on  the 
necessity  of  accurate  observation,  we  must  beware  of 
rushing  to  the  opposite  extreme,  and  supposing  that 
observation  alone  is  enough.  Observation,  the  accu- 
rate use  of  the  senses  (by  which  we  must  understand 
inner  as  well  as  outer  sense),  is  not  the  whole  work  of 
Science.  We  may  stare  at  facts  every  minute  of  our 
waking  day  without  being  a  whit  the  wiser  unless  we 
exert  our  intellects  to  build  upon  them  or  under  them. 
To  make  our  examination  fruitful,  we  must  have 
conceptions,  theories,  speculations,  to  bring  to  the  test. 
The  comparison  of  these  with  the  facts  is  the  inductive 
verification  of  them.  Science  has  to  exercise  its 
ingenuity  both  in  making  hypotheses  and  in  contriving 
occasions  for  testing  them  by  observation.  These 
contrived  occasions  are  its  artificial  experiments,  which 
have  come  to  be  called  experiments  simply  by  contrast 
with  conclusive  observations  for  which  Nature  herself 
furnishes  the  occasion.  The  observations  of  Science 
are  not  passive  observations.  The  word  experiment 
simply  means  trial,  and  every  experiment,  natural  or 
artificial,  is  the  trial  of  a  hypothesis.  In  the  language 
of  Leonardo  da  Vinci,  "  Theory  is  the  general,  Experi- 
ments are  the  soldiers  ". 

Observation  and  Inference  go  hand  in  hand  in  the 
work  of  Science,  but  with  a  view  to  a  methodical 
exposition  of  its  methods,  we  may  divide  them  broadly 
into  Methods  of  Observation  and  Methods  of  Inference. 
There  are  errors  specially  incident  to  Observation,  and 
errors  specially  incident  to  Inference.  How  to  observe 
correctly  and  how  to  make  correct  inferences  from  our 
observations  are  the  two  objects  of  our  study  in  Induc- 
tive Logic :  we  study  the  examples  of  Science  because 


272         Inductive  Logic,  or  the  Logic  of  Science. 

they    have    been    successful    in    accomplishing    those 
objects. 

That  all  inference  to  the  unobserved  is  founded  on 
facts,  on  the  data  of  experience,  need  not  be  postulated. 
It  is  enough  to  say  that  Inductive  Logic  is  concerned 
with  inference  in  so  far  as  it  is  founded  on  the  data  of 
experience.  But  inasmuch  as  all  the  data  of  experi- 
ence are  not  of  equal  value  as  bases  of  inference,  it  is 
well  to  begin  with  an  analysis  of  them,  if  we  wish  to 
take  a  comprehensive  survey  of  the  various  modes  of 
inference  and  the  conditions  of  their  validity. 


CHAPTER  I. 

THE  DATA  OF  EXPERIENCE  AS  GROUNDS  OF 
INFERENCE  OR  RATIONAL  BELIEF. 

IF  we  examine  any  of  the  facts  or  particulars  on  which 
an  inference  to  the  unobserved  is  founded,  we  shall 
find  that  they  are  not  isolated  individuals  or  attributes, 
separate  objects  of  perception  or  thought,  but  relations 
among  things  and  their  qualities,  constituents,  or 
ingredients. 

Take  the  "particular"  from  which  Mill's  village 
matron  inferred,  the  fact  on  which  she  based  her 
expectation  of  a  cure  for  her  neighbour's  child.  It  is  a 
relation  between  things.  We  have  the  first  child's 
ailment,  the  administration  of  the  drug,  and  the 
recovery,  a  series  of  events  in  sequence.  This  observed 
sequence  is  the  fact  from  which  she  is  said  to  infer,  the 
datum  of  experience.  She  expects  this  sequence  to 
be  repeated  in  the  case  of  her  neighbour's  child. 

Similarly  we  shall  find  that,  in  all  cases  where  we 
infer,  the  facts  are  complex,  are  not  mere  isolated 
things,  but  relations  among  things — using  the  word 
thing  in  its  widest  sense — relations  which  we  expect  to 
find  repeated,  or  believe  to  have  occurred  before,  or  to 
be  occurring  now  beyond  the  range  of  our  observation. 
These  relations,  which  we  may  call  coincidences  or 
conjunctions,  are  the  data  of  experience  from  which  we 
18  (273) 


274         Inductive  Logic,  or  the  Logic  of  Science. 

start  in  our  beliefs  or  inferences  about  the  unex- 
perienced. 

The  problem  of  Inductive  Logic  being  to  determine 
when  or  on  what  conditions  such  beliefs  are  rational, 
we  may  begin  by  distinguishing  the  data  of  coincidence 
or  conjunction  accordingly.  There  are  certain  coinci- 
dences that  we  expect  to  find  repeated  beyond  the 
occasions  on  which  we  have  observed  them,  and  others 
that  we  do  not  expect  to  find  repeated.  If  it  is  a  sound 
basis  of  inference  that  we  are  in  search  of,  it  is  evidently 
to  these  first,  the  coincidences  that  we  are  assured  of 
finding  again,  that  we  must  direct  our  study.  Let  us 
see  whether  they  can  be  specified. 

(i)  If  there  is  no  causal  connexion  between  A  and 
B,  using  these  as  symbols  for  the  members  of  a 
coincidence — the  objects  that  are  presented  together — 
we  do  not  expect  the  coincidence  to  be  repeated.  If  A 
and  B  are  connected  as  cause  and  effect,  we  expect  the 
effect  to  recur  in  company  with  the  cause.  We  expect 
that  when  the  cause  reappears  in  similar  circumstances, 
the  effect  also  will  reappear. 

You  are  hit,  e.g.,  by  a  snowball,  and  the  blow  is 
followed  by  a  feeling  of  pain.  The  sun,  we  shall 
say,  was  shining  at  the  moment  of  the  impact  of  the 
snowball  on  your  body.  The  sunshine  preceded  your 
feeling  of  pain  as  well  as  the  blow.  But  you  do  not 
expect  the  pain  to  recur  next  time  that  the  sun  shines. 
You  do  expect  it  to  recur  next  time  you  are  hit  by  a 
snowball. 

The  taking  of  food  and  a  certain  feeling  of  strength 
are  causally  connected.  If  we  go  without  food,  we  are 
not  surprised  when  faintness  or  weariness  supervenes. 

Suppose  that  when  our  village  matron  administered 
her  remedy  to  her  own  child,  a  dog  stood  by  the 


Experience  as  ground  of  Inference  or  Rational  Belief.   275 

bedside  and  barked.  The  barking  in  that  case  would 
precede  the  cure.  Now,  if  the  matron  were  what  we 
should  call  a  superstitious  person,  and  believed  that 
this  concomitant  had  a  certain  efficacy,  that  the  dog's 
barking  and  the  cure  were  causally  connected,  she 
would  take  the  dog  with  her  when  she  went  to  cure 
her  neighbour's  child.  Otherwise  she  would  not.  She 
would  say  that  the  barking  was  an  accidental,  casual, 
fortuitous  coincidence,  and  would  build  no  expectation 
upon  it. 

These  illustrations  may  serve  to  remind  us  of  the 
familiar  fact  that  the  causal  nexus  is  at  least  one  of 
the  things  that  we  depend  on  in  our  inferences  to  the 
unobserved.  To  a  simple  sequence  we  attach  no 
importance,  but  a  causal  sequence  or  consequence  that 
has  been  observed  is  a  mainstay  of  inference. 

Whether  the  causal  sequence  holds  or  not  as  a 
matter  of  fact,  we  depend  upon  it  if  we  believe  in  it  as 
a  matter  of  fact.  But  unless  it  does  hold  as  a  matter 
of  fact,  it  is  valueless  as  a  guide  to  the  unknown,  and 
our  belief  is  irrational.  Clearly,  therefore,  if  rational 
belief  is  what  we  aim  at,  it  is  of  importance  that  we 
should  make  sure  of  cause  and  effect  as  matter  of  fact 
in  the  sequence  of  events. 

One  large  department  of  Inductive  Logic,  the  so- 
called  Experimental  Methods,  is  designed  to  help  us  in 
thus  making  sure,  i.e.,  in  ascertaining  causal  sequence 
as  a  matter  of  fact.  It  is  assumed  that  by  careful 
observation  of  the  circumstances,  we  can  distinguish 
between  mere  simple  sequence  and  causal  sequence  or 
consequence,  and  methods  are  recommended  of  ob- 
serving with  the  proper  precautions  against  error. 

Observe  that  these  methods,  though  called  Inductive, 
are  not  concerned  with  arriving  at  general  propositions. 


276         Inductive  Logic,  or  the  Logic  of  Science. 

The  principle  we  go  upon  is  simply  this,  that  if  it  can  be 
ascertained  as  matter  of  fact  that  a  certain  thing  is 
related  to  another  as  cause  and  effect,  we  may  count 
upon  the  same  relation  as  holding  in  unobserved 
Nature,  on  the  general  ground  that  like  causes  produce 
like  effects  in  like  circumstances. 

Observe,  also,  that  I  deliberately  speak  of  the  causal 
relation  as  a  relation  among  phenomena.  Whether 
this  use  of  the  words  cause  and  effect  is  philosophically 
justifiable,  is  a  question  that  will  be  raised  and  partly 
discussed  later  on.  Here  I  simply  follow  the  common 
usage,  in  accordance  with  which  objects  of  perception, 
e.g.,  the  administration  of  a  drug  and  the  recovery  of 
a  patient,  are  spoken  of  as  cause  and  effect.  Such 
observable  sequences  are  causal  sequences  in  the 
ordinary  sense,  and  it  is  part  of  the  work  of  Science  to 
observe  them.  I  do  not  deny  that  the  true  cause,  or 
the  cause  that  science  aims  ultimately  at  discovering, 
is  to  be  found  in  the  latent  constitution  or  composition 
of  the  things  concerned.  Only  that,  as  we  shall  see 
more  precisely,  is  a  cause  of  another  description. 
Meantime,  let  us  take  the  word  to  cover  what  it 
undoubtedly  covers  in  ordinary  speech,  the  perceptible 
antecedent  of  a  perceptible  consequent. 

Strictly  speaking,  as  we  shall  find,  Science  has  only 
one  method  of  directly  observing  when  events  are  in 
causal  sequence.  But  there  are  various  indirect 
methods,  which  shall  be  described  in  some  sort  of 
order. 

For  the  practical  purposes  of  life,  a  single  ascertained 
causal  sequence  is  of  little  value  as  a  basis  of  inference, 
because  we  can  infer  only  to  its  repetition  in  identical 
circumstances.  Suppose  our  village  matron  had  been 
able  to  ascertain  as  a  matter  of  fact — a  feat  as  we  shall 


Experience  as  ground  of  Inference  or  Rational  Belief.    277 

find  not  to  be  achieved  by  direct  observation — that  the 
drug  did  cure  her  child,  this  knowledge  by  itself  would 
have  been  practically  valueless,  because  the  only 
legitimate  inference  would  have  been  that  an  exactly 
similar  dose  would  have  the  same  effect  in  exactly 
similar  circumstances.  But,  as  we  shall  find,  though 
practically  valueless,  a  single  ascertained  causal 
sequence  is  of  supreme  value  in  testing  scientific 
speculations  as  to  the  underlying  causes. 

(2)  We  have  next  to  see  whether  there  are  any  other 
rational  expectations  based  on  observed  facts.  We 
may  lay  down  as  a  principle  the  following : — 

If  a  conjunction  or  coincidence  has  constantly  been 
repeated  within  our  experience,  we  expect  it  to  recur  and 
believe  that  it  has  recurred  outside  our  experience. 

How  far  such  expectations  are  rational,  and  with 
what  degrees  of  confidence  they  should  be  entertained, 
are  the  questions  for  the  Logic  of  Inference,  but 
we  may  first  note  that  we  do  as  a  matter  of  habit 
found  expectations  on  repeated  coincidence,  and  indeed 
guide  our  daily  life  in  this  way.  If  we  meet  a  man 
repeatedly  in  the  street  at  a  certain  hour,  we  go  out 
expecting  to  meet  him  :  it  is  a  shock  to  our  expectations, 
a  surprise,  when  we  do  not.  If  we  are  walking  along 
a  road  and  find  poles  set  up  at  regular  intervals,  we 
continue  our  walk  expection  to  find  a  pole  coincident 
with  the  end  of  each  interval. 

What  Mill  calls  the  uniformities  of  Nature,  the  uni- 
formities expressed  in  general  propositions,  are  from 
the  point  of  view  of  the  observer,  examples  of  repeated 
coincidence.  Birth,  growth,  decay,  death,  are  not 
isolated  or  variable  coincidences  with  organised  being  : 
all  are  born,  all  grow,  all  decay,  and  all  die.  These 
uniformities  constitute  the  order  of  Nature  :  the  coinci- 


278         Inductive  Logic,  or  the  Logic  of  Science. 

dences  observed  are  not  occasional,  occurring  once  in 
a  way  or  only  now  and  then  ;  they  turn  up  again  and 
again.  Trees  are  among  the  uniformities  on  the 
varied  face  of  Nature :  certain  relations  between  the 
soil  and  the  plant,  between  trunk,  branches,  and  leaves 
are  common  to  them.  For  us  who  observe,  each 
particular  tree  that  comes  under  our  observation  is  a 
repetition  of  the  coincidence.  And  so  with  animals  : 
in  each  we  find  certain  tissues,  certain  organs,  con- 
joined on  an  invariable  plan. 

Technically  these  uniformities  have  been  divided 
into  uniformities  of  Sequence  and  uniformities  of 
Coexistence.  Thus  the  repeated  alternation  of  day 
and  night  is  a  uniformity  of  Sequence :  the  invariable 
conjunction  of  inertia  with  weight  is  a  uniformity  of 
Coexistence.  But  the  distinction  is  really  immaterial 
to  Logic.  What  Logic  is  concerned  with  is  the  obser- 
vation of  the  facts  and  the  validity  of  any  inference 
based  on  them  :  and  in  these  respects  it  makes  no 
difference  whether  the  uniformity  that  we  observe  and 
found  upon  is  one  of  Sequence  or  of  Coexistence. 

It  was  exclusively  to  such  inferences,  inferences 
from  observed  facts  of  repeated  coincidence,  that  Mill 
confined  himself  in  his  theory  of  Induction,  though  not 
in  his  exposition  of  the  methods.  These  are  the 
inferences  for  which  we  must  postulate  what  he  calls 
the  Uniformity  of  Nature.  Every  induction,  he  says, 
following  Whately,  may  be  thrown  into  the  form  of  a 
Syllogism,  in  which  the  principle  of  the  Uniformity  of 
Nature  is  the  Major  Premiss,  standing  to  the  inference 
in  the  relation  in  which  the  Major  Premiss  of  a 
Syllogism  stands  to  the  conclusion.  If  we  express  this 
abstractly  denominated  principle  in  prepositional  form, 
and  take  it  in  connexion  with  Mill's  other  saying  that 


Experience  as  ground  of  Inference  or  Rational  Belief.    279 

the  course  of  Nature  is  not  a  uniformity  but  uniformities, 
we  shall  find,  I  think,  that  this  postulated  Major 
Premiss  amounts  to  an  assumption  that  the  observed 
Uniformities  of  Nature  continue.  Mill's  Inductive 
Syllogism  thus  made  explicit  would  be  something  like 
this  :— 

All  the  observed  uniformities  of  Nature  continue. 
That  all  men  have  died  is  an  observed  uniformity. 
Therefore,  it  continues ;  i.e.,  all  men  will  die  and  did  die 
before  the  beginning  of  record. 

There  is  no  doubt  that  this  is  a  perfectly  sound 
postulate.  Like  all  ultimate  postulates  it  is  indemon- 
strable ;  Mill's  derivation  of  it  from  Experience  did  not 
amount  to  a  demonstration.  It  is  simply  an  assump- 
tion on  which  we  act.  If  any  man  cares  to  deny  it, 
there  is  no  argument  that  we  can  turn  against  him. 
We  can  only  convict  him  of  practical  inconsistency,  by 
showing  that  he  acts  upon  this  assumption  himself 
every  minute  of  his  waking  day.  If  we  do  not  believe 
in  the  continuance  of  observed  uniformities,  why  do  we 
turn  our  eyes  to  the  window  expecting  to  find  it  in  its 
accustomed  order  of  place  ?  Why  do  we  not  look  for 
it  in  another  wall  ?  Why  do  we  dip  our  pens  in  ink, 
and  expect  the  application  of  them  to  white  paper  to 
be  followed  by  a  black  mark  ? 

The  principle  is  sound,  but  is  it  our  only  postulate 
in  inference  to  the  unobserved,  and  does  the  continu- 
ance of  empirical  laws  represent  all  that  Science 
assumes  in  its  inferences  ?  Mill  was  not  satisfied 
about  this  question.  He  pointed  out  a  difficulty  which 
a  mere  belief  in  empirical  continuity  does  not  solve. 
Why  do  we  believe  more  confidently  in  some  uniformi- 
ties than  in  others  ?  Why  would  a  reported  breach  of 


280         Inductive  Logic,  or  the  Logic  of  Science. 

one  be  regarded  with  more  incredulity  than  that  of 
another  ?  Suppose  a  traveller  to  return  from  a  strange 
country  and  report  that  he  had  met  men  with  heads 
growing  beneath  their  shoulders,  why  would  this  be 
pronounced  more  incredible  than  a  report  that  he  had 
seen  a  grey  crow  ?  All  crows  hitherto  observed  have 
been  black,  and  in  all  men  hitherto  observed  the  heads 
have  been  above  the  shoulders  :  if  the  mere  continuity 
of  observed  uniformities  is  all  that  we  go  upon  in  our 
inferences,  a  breach  of  the  one  uniformity  should  be 
just  as  improbable  as  a  breach  of  the  other,  neither 
more  nor  less.  Mill  admitted  the  difficulty,  and 
remarked  that  whoever  could  solve  it  would  have 
solved  the  problem  of  Induction.  Now  it  seems  to  me 
that  this  particular  difficulty  may  be  solved,  and  yet 
leave  another  behind.  It  may  be  solved  within  the 
limits  of  the  principle  of  empirical — meaning  by  that 
observational — continuity.  The  uniform  blackness  of 
the  crow  is  an  exception  within  a  wider  uniformity : 
the  colour  of  animals  is  generally  variable.  Hence  we 
are  not  so  much  surprised  at  the  reported  appearance 
of  a  grey  crow :  it  is  in  accordance  with  the  more 
general  law.  On  the  other  hand,  the  uniform  position 
of  the  head  relative  to  other  parts  of  the  body  is  a 
uniformity  as  wide  as  the  animal  kingdom  :  it  is  a 
coincidence  repeated  as  often  as  animals  have  been 
repeated,  and  merely  on  the  principle  that  uniformities 
continue,  it  has  an  absolutely  uncontradicted  series  in 
its  favour. 

But  is  this  principle  really  all  that  we  assume  ?  Do 
we  not  also  assume  that  behind  the  observed  fact  of 
uniformity,  there  is  a  cause  for  it,  a  cause  that  does 
not  appear  on  the  surface  of  the  observation,  but  must 
be  sought  outside  of  its  range  ?  And  do  not  the  various 


Experience  as  ground  of  Inference  or  Rational  Belief.    281 

degrees  of  confidence  with  which  we  expect  a  repetition 
of  the  coincidence,  depend  upon  the  extent  of  our 
knowledge  of  the  producing  causes  and  the  mode  of 
their  operation  ?  At  bottom  our  belief  in  the  continu- 
ance of  the  observed  uniformities  rests  on  a  belief  in 
the  continuance  of  the  producing  causes,  and  till  we 
know  what  these  are  our  belief  has  an  inferior  warrant : 
there  is  less  reason  for  our  confidence. 

To  go  back  to  the  illustrations  with  which  we 
started.  If  we  have  met  a  man  every  day  for  months 
at  a  certain  place  at  a  certain  hour,  it  is  reasonable  to 
expect  to  meet  him  there  to-morrow,  even  if  our  know- 
ledge does  not  go  beyond  the  observed  facts  of  repeated 
coincidence.  But  if  we  know  also  what  brings  him 
there,  and  that  this  cause  continues,  we  have  a  stronger 
reason  for  our  expectation.  And  so  with  the  case  of 
poles  at  regular  intervals  on  a  road.  If  we  know  why 
they  are  placed  there,  and  the  range  of  the  purpose, 
we  expect  their  recurrence  more  confidently  within  the 
limits  of  that  purpose.  This  further  knowledge  is  a 
warrant  for  stronger  confidence,  because  if  we  know 
the  producing  causes,  we  are  in  a  better  position  for 
knowing  whether  anything  is  likely  to  defeat  the 
coincidence.  A  uniformity  is  said  to  be  explained 
when  its  cause  is  known,  and  an  inference  from  an 
explained  uniformity  is  always  more  certain  than  an 
inference  from  a  uniformity  that  is  merely  empirical  in 
the  sense  of  being  simply  observed. 

Now,  the  special  work  of  Science  is  to  explain,  in 
the  sense  of  discovering  the  causes  at  work  beneath 
what  lies  open  to  observation.  In  so  doing  it  follows 
a  certain  method,  and  obeys  certain  conditions  of 
satisfactory  explanation.  Its  explanations  are  infer- 
ences from  facts,  inasmuch  as  it  is  conformity  with 


282         Inductive  Logic,  or  the  Logic  of  Science. 

observed  facts,  with  outward  signs  of  underlying  causal 
nexus,  that  is  the  justification  of  them.  But  they  are 
not  inferences  from  facts  in  the  sense  above  described 
as  empirical  inference.  In  its  explanations  also 
Science  postulates  a  principle  that  may  be  called  the 
Uniformity  of  Nature.  But  this  principle  is  not 
merely  that  observed  uniformities  continue.  It  may  be 
expressed  rather  as  an  assumption  that  the  underlying 
causes  are  uniform  in  their  operation,  that  as  they  have 
acted  beneath  the  recorded  experiences  of  mankind,  so 
they  have  acted  before  and  will  continue  to  act. 

The  foregoing  considerations  indicate  a  plan  for  a 
roughly  systematic  arrangement  of  the  methods  of 
Induction.  Seeing  that  all  inference  from  the  data  of 
experience  presupposes  causal  connexion  among  the 
data  from  which  we  infer,  all  efforts  at  establishing 
sound  bases  of  inference,  or  rational  ground  for  expec- 
tation fall,  broadly  speaking,  under  two  heads :  (i) 
Methods  of  ascertaining  causal  connexion  among 
phenomena  as  a  matter  of  fact,  that  is,  Methods  of 
Observation  ;  and  (2)  Methods  of  ascertaining  what 
the  causal  connexion  is,  that  is,  Methods  of  Explanation. 

These  constitute  the  body  of  Inductive  Logic.  But 
there  is  a  preliminary  and  a  pendant.  Without 
raising  the  question  of  causal  connexion,  we  are  liable 
to  certain  errors  in  ascertaining  in  what  sequence 
and  with  what  circumstances  events  really  occurred. 
These  tendencies  to  error  deserve  to  be  pointed  out  by 
way  of  warning,  and  this  I  shall  attempt  in  a  separate 
chapter  on  observation  of  facts  of  simple  sequence. 
This  is  preliminary  to  the  special  methods  of  observing 
causal  sequence.  Then,  by  way  of  pendant,  I  shall 
consider  two  modes  of  empirical  inference  from  data  in 


Experience  as  ground  of  Inference  or  Rational  Belief.   283 

which  the  causal  connexion  has  not  been  ascertained 
or  explained — Inference  from  approximate  generalisa- 
tions to  particular  cases,  and  Inference  from  Analogy. 
Most  of  these  methods  in  one  form  or  another  were 
included  by  Mill  in  his  system  of  Inductive  Logic,  and 
the  great  merit  of  his  work  was  that  he  did  include  them, 
though  at  some  sacrifice  of  consistency  with  his  intro- 
ductory theory.  With  regard  to  the  kind  of  empirical 
inference  which  that  theory,  following  the  lead  of 
Whately,  took  as  the  type  of  all  inference,  Logic  has 
really  little  to  say.  It  was  this  probably  that  was  in 
Mill's  mind  when  he  said  that  there  is  no  Logic  of 
Observation,  ignoring  the  fact  that  the  Experimental 
Methods  are  really  methods  of  observation,  as  well  as 
the  Methods  of  Eliminating  Chance  by  calculation  of 
Probability.  There  is  no  method  of  observing  uni- 
formities except  simply  observing  them.  Nor  indeed 
is  there  any  "  method  "  of  inferring  from  them :  we 
can  only  point  out  that  in  every  particular  inference 
from  them  we  assume  or  postulate  their  continuance 
generally.  As  regards  their  observation,  we  may  point 
out  further  that  a  special  fallacy  is  incident  to  it,  the 
fallacy  of  ignoring  exceptions.  If  we  are  prepossessed 
or  prejudiced  in  favour  of  a  uniformity,  we  are  apt  to 
observe  only  the  favourable  instances,  and  to  be  blind 
to  cases  where  the  supposed  invariable  coincidence 
does  not  occur.  Thus,  as  Bacon  remarked  among  his 
Idola,  we  are  apt  to  remember  when  our  dreams  come 
true,  and  to  forget  when  they  do  not.  Suppose  we 
take  up  the  notion  that  a  new  moon  on  a  Saturday  is 
invariably  followed  by  twenty  days  of  unsettled 
weather,  one  o*  two  or  a  few  cases  in  which  this  notably 
holds  good  are  apt  to  be  borne  in  mind,  while  cases 
where  the  weather  is  neither  conspicuously  good  nor 


284         Inductive  Logic,  or  the  Logic  of  Science. 

bad  are  apt  to  be  overlooked.  But  when  a  warning 
has  been  given  against  this  besetting  fallacy,  Logic 
has  nothing  further  to  say  about  empirical  uniformities, 
except  that  we  may  infer  from  them  with  some  degree 
of  reasonable  probability,  and  that  if  we  want  ground 
for  a  more  certain  inference  we  should  try  to  explain 
them. 


CHAPTER  II. 

ASCERTAINMENT  OF  SIMPLE  FACTS  IN  THEIR  ORDER. 
—PERSONAL  OBSERVATION.— HEARSAY  EVIDENCE 
—METHOD  OF  TESTING  TRADITIONAL  EVIDENCE. 

ALL  beliefs  as  to  simple  matter  of  fact  must  rest 
ultimately  on  observation.  But,  of  course,  we  believe 
many  things  to  have  happened  that  we  have  never 
seen.  As  Chaucer  says  : — 

But  God  forbede  but  men  shoulde  'lieve 
Wei  more  thing  than  men  han  seen  with  e^e. 
Man  shall  not  weenen  everything  a  lie 
But  if  himself  it  seeth  or  else  doth. 

For  the  great  bulk  of  matters  of  fact  that  we  believe 
we  are  necessarily  dependent  on  the  observations  of 
others.  And  if  we  are  to  apply  scientific  method  to 
the  ascertainment  of  this,  we  must  know  what  errors 
we  are  liable  to  in  our  recollections  of  what  we  have 
ourselves  witnessed,  and  what  errors  are  apt  to  arise  in 
the  tradition  of  what  purports  to  be  the  evidence  of 
eye-witnesses. 


I. — PERSONAL  OBSERVATION. 

It  is  hard  to  convince  anybody  that  he  cannot  trust 
implicitly  to  his  memory  of  what  he  has  himself  seen. 


286         Inductive  Logic ,  or  the  Logic  of  Science. 

We  are  ready  enough  to  believe  that  others  may  be 
deceived :  but  not  our  own  senses.  Seeing  is  believing. 
It  is  well,  however,  that  we  should  realise  that  all 
observation  is  fallible,  even  our  own. 

Three  great  besetting  fallacies  or  tendencies  to  error 
may  be  specified  : — 

1.  Liability  to  have  the  attention  fastened  on  special 
incidents,    and    so   diverted   from    other  parts  of  the 
occurrence. 

2.  Liability  to  confuse  and  transpose  the  sequence 
of  events. 

3.  Liability  to  substitute  inference  for  fact. 

It  is  upon  the  first  of  these  weaknesses  m  man  as 
an  observing  machine  that  jugglers  chiefly  depend  on 
working  their  marvels.  Sleight  of  hand  counts  for 
much,  but  diverting  the  spectator's  eyes  for  a  good 
deal  more.  That  is  why  they  have  music  played  and 
patter  incessantly  as  they  operate.  Their  patter  is  not 
purposeless  :  it  is  calculated  to  turn  our  eyes  away 
from  the  movements  of  their  nimble  hands. 

It  must  be  borne  in  mind  that  in  any  field  of  vision 
there  are  many  objects,  and  that  in  any  rapid  succession 
of  incidents  much  more  passes  before  the  eyes  than  the 
memory  can  retain  in  its  exact  order.  It  is  of  course 
in  moments  of  excitement  and  hurry,  when  our  obser- 
vation is  distracted,  that  we  are  most  subject  to 
fallacious  illusions  of  memory.  Unconsciously  we 
make  a  coherent  picture  of  what  we  have  seen,  and 
very  often  it  happens  that  the  sequence  of  events  is 
not  what  actually  passed,  but  what  we  were  prejudiced 
in  favour  of  seeing.  Hence  the  unlikelihood  of  finding 
exact  agreement  among  the  witnesses  of  any  exciting 
occurrence,  a  quarrel,  a  railway  accident,  a  collision  at 
sea,  the  incidents  of  a  battle. 


Ascertainment  of  Simple  Facts  in  their  Order.    287 

"  It  commonly  happens,"  says  Mr.  Kinglake,1  "  that 
incidents  occurring  in  a  battle  are  told  by  the  most 
truthful  bystanders  with  differences  more  or  less  wide." 
In  the  attack  on  the  Great  Redoubt  in  the  Battle  of  the 
Alma,  a  young  officer,  Anstruther,  rushed  forward  and 
planted  the  colours  of  the  Royal  Welsh — but  where  ? 
Some  distinctly  remembered  seeing  him  dig  the  butt- 
end  of  the  flagstaff  into  the  parapet :  others  as  distinctly 
remembered  seeing  him  fall  several  paces  before  he 
reached  it.  Similarly  with  the  incidents  of  the  death  of 
the  Prince  Imperial  near  the  Italezi  Hills  in  the  Zulu 
War.  He  was  out  as  a  volunteer  with  a  reconnoitring 
party.  They  had  off-saddled  at  a  kraal  and  were 
resting,  when  a  band  of  Zulus  crept  up  through  the 
long  grass,  and  suddenly  opened  fire  and  made  a  rush 
forward.  Our  scouts  at  once  took  horse,  as  a  recon- 
noitring party  was  bound  to  do,  and  scampered  off, 
but  the  Prince  was  overtaken  and  killed.  At  the 
Court-Martial  which  ensued,  the  five  troopers  gave 
the  most  conflicting  accounts  of  particulars  which  an 
unskilled  investigator  would  think  could  not  possibly 
have  been  mistaken  by  eye-witnesses  of  the  same  event. 
One  said  that  the  Prince  had  given  the  order  to  mount 
before  the  Zulus  fired  :  another  that  he  gave  the  order 
directly  after  :  a  third  was  positive  that  he  never  gave 
the  order  at  all,  but  that  it  was  given  after  the  surprise 
by  the  officer  in  command.  One  said  that  he  saw  the 
Prince  vault  into  the  saddle  as  he  gave  the  order  : 
another  that  his  horse  bolted  as  he  laid  hold  of  the 
saddle,  and  that  he  ran  alongside  trying  to  get  up. 

The  evidence  before  any  Court  of  Inquiry  into  an 
exciting  occurrence  is  almost  certain  to  reveal  similar 

1  The  Invasion  of  the  Crimea^  iii.  124 


288         Inductive  Logic ;  or  the  Logic  of  Science. 

discrepancies.  But  what  we  find  it  hard  to  realise  is 
that  we  ourselves  can  possibly  be  mistaken  in  what 
we  have  a  distinct  and  positive  recollection  of  having 
seen.  It  once  happened  to  myself  in  a  London  street 
to  see  a  drunken  woman  thrown  under  a  cab  by  her 
husband.  Two  cabs  were  running  along,  a  four- 
wheeler  and  a  hansom  :  the  woman  staggered  almost 
under  the  first,  and  was  thrown  under  the  second.  As 
it  happened  the  case  never  got  beyond  the  police 
station  to  which  the  parties  were  conveyed  after 
fierce  opposition  from  some  neighbours,  who  sympa- 
thised entirely  with  the  man.  The  woman  herself, 
when  her  wounds  were  dressed,  acknowledged  the 
justice  of  her  punishment,  and  refused  to  charge  her 
husband.  I  was  all  the  more  willing  to  acquiesce  in 
this  because  I  found  that  while  I  had  the  most  distinct 
impression  of  having  seen  the  four-wheeler  run  over  the 
woman's  body,  and  should  have  been  obliged  to  swear 
accordingly,  there  could  be  no  doubt  that  it  was  really 
the  hansom  that  had  done  so.  This  was  not  only  the 
evidence  of  the  neighbours,  which  I  suspected  at  the  time 
of  being  a  trick,  but  of  the  cabdriver,  who  had  stopped 
at  the  moment  to  abide  the  results  of  the  accident.  I 
afterwards  had  the  curiosity  to  ask  an  eminent  police 
magistrate,  Sir  John  Bridge,  whether  this  illusion  of 
memory  on  my  part — which  I  can  only  account  for  by- 
supposing  that  my  eyes  had  been  fixed  on  the  sufferer 
and  that  I  had  unconsciously  referred  her  injuries  to 
the  heavier  vehicle — would  have  entirely  discredited 
my  testimony  in  his  Court.  His  answer  was  that  it 
would  not ;  that  he  was  constantly  meeting  with  such 
errors,  and  that  if  he  found  a  number  of  witnesses  of 
the  same  occurrence  exactly  agreed  in  every  particular, 
he  would  suspect  that  they  had  talked  the  matter  over 


Ascertainment  of  Simple  Facts  in  their  Order.   289 

and  agreed  upon  what  they  were  to  say.  This  was 
the  opinion  of  an  experienced  judge,  a  skilled  critic  of 
the  defects  of  personal  observation.  An  Old  Bailey 
counsel  for  the  defence,  who  is  equally  acquainted  with 
the  weakness  of  human  memory,  takes  advantage  of 
the  fact  that  it  is  not  generally  understood  by  a  Jury, 
and  makes  the  fallacious  assumption  that  glaring 
discrepancies  are  irreconcilable  with  the  good  faith  of 
the  witnesses  who  differ.1 

II. — TRADITION. — HEARSAY  EVIDENCE. 

Next  in  value  to  personal  observation,  we  must  place 
the  report,  oral  or  written,  of  an  eye-witness.  This  is 
the  best  evidence  we  can  get  if  we  have  not  witnessed 
an  occurrence  ourselves.  Yet  Courts  of  Law,  which 
in  consideration  of  the  defects  of  personal  observation 
require  more  than  one  witness  to  establish  the  truth, 
exclude  hearsay  evidence  altogether  in  certain  cases, 
and  not  without  reason. 

1  The  truth  is,  that  we  see  much  less  than  is  commonly  sup- 
posed. Not  every  impression  is  attended  to  that  is  made  on  the 
retina,  and  unless  we  do  attend  we  cannot,  properly  speaking,  be 
said  to  see.  Walking  across  to  college  one  day,  I  was  startled  by 
seeing  on  the  face  of  a  clock  in  my  way  that  it  was  ten  minutes  to 
twelve,  whereas  I  generally  passed  that  spot  about  twenty  minutes 
to  twelve.  I  hurried  on,  fearing  to  be  late,  and  on  my  arrival 
found  myself  in  very  good  time.  On  my  way  back,  passing  the 
clock  again,  I  looked  up  to  see  how  much  it  was  fast.  It  marked 
ten  minutes  to  eight.  It  had  stopped  at  that  time.  When  I 
passed  before  I'  had  really  seen  only  the  minute  hand.  The  whole 
dial  must  have  been  on  my  retina,  but  I  had  looked  at  or  attended 
to  only  what  I  was  in  doubt  about,  taking  the  hour  for  granted. 
I  am  bound  to  add  that  my  business  friends  hint  that  it  is  only 
absorbed  students  that  are  capable  of  such  mistakes,  and  that  alert 
men  of  business  are  more  circumspect.  That  can  only  be  because 
they  are  more  alive  to  the  danger  of  error. 


290          Inductive  Logic,  or  the  Logic  of  Science. 

In  hearing  a  report  we  are  in  the  position  of  observers 
of  a  series  of  significant  sounds,  and  we  are  subject  to  all 
the  fallacies  of  observation  already  mentioned.  In  an 
aggravated  degree,  for  words  are  harder  to  observe  than 
visible  things.  Our  attention  is  apt  to  be  more  listless 
than  in  presence  of  the  actual  events.  Our  minds  dwell 
upon  parts  of  the  narrative  to  the  neglect  of  other  parts, 
and  in  the  coherent  story  or  description  that  we  retain 
in  our  memories,  sequences  are  apt  to  be  altered  and 
missing  links  supplied  in  accordance  with  what  we 
were  predisposed  to  hear.  Thus  hearsay  evidence  is 
subject  to  all  the  imperfections  of  the  original  observer, 
in  addition  to  the  still  more  insidious  imperfections  of 
the  second  observer. 

How  quickly  in  the  course  of  a  few  such  transmissions- 
hearsay  loses  all  evidentiary  value  is  simply  illustrated 
by  the  game  known  as  Russian  Scandal.  One  of  a 
company,  A,  writes  down  a  short  tale  or  sketch,  and 
reads  it  to  B.  B  repeats  it  to  C,  C  to  D,  and  so  on. 
When  it  has  thus  gone  the  round  of  the  company,  the 
last  hearer  writes  down  his  version,  and  it  is  compared 
with  the  original.  With  every  willingness  to  play  fair, 
the  changes  are  generally  considerable  and  significant. 

Sometimes  it  is  possible  to  compare  an  oral  tradition 
with  a  contemporary  written  record.  In  one  of  Mr. 
Hayward's  Essays — "  The  Pearls  and  Mock  Pearls  of 
History  " — there  are  some  examples  of  this  disenchant- 
ing process.  There  is,  for  instance,  a  pretty  story  of 
an  exchange  of  courtesies  between  the  leaders  of  the 
French  and  English  Guards  at  the  battle  of  Fontenoy. 
The  tradition  runs  that  Lord  Charles  Hay  stepped 
in  front  of  his  men  and  invited  the  French  Guards 
to  fire,  to  which  M.  d'Auteroche  with  no  less 
chivalry  responded  :  "  Monsieur,  we  never  fire  first ; 


Ascertainment  of  Simple  Facts  in  their  Order.   291 

you  fire  ".  What  really  passed  we  learn  from  a  letter 
from  Lord  Charles  Hay  to  his  mother,  which  happens 
to  have  been  preserved.  "  I  advanced  before  our 
regiment,  and  drank  to  the  Frenchmen,  and  told  them 
we  were  the  English  Guards,  and  hoped  they  would 
stand  till  we  came,  and  not  swim  the  Scheldt  as  they 
did  the  Maine  at  Dettingen."  Tradition  has  changed 
this  lively  piece  of  buffoonery  into  an  act  of  stately  and 
romantic  courtesy.  The  change  was  probably  made 
quite  unconsciously  by  some  tenth  or  hundredth 
transmitter,  who  remembered  only  part  of  the  story, 
and  dressed  the  remainder  to  suit  his  own  fancy. 

The  question  has  been  raised,  For  how  long  can  oral 
tradition  be  trusted  ?  Newton  was  of  opinion  that  it 
might  be  trusted  for  eighty  years  after  the  event. 
Others  have  named  forty  years.  But  if  this  means 
that  we  may  believe  a  story  that  we  find  in  circulation 
forty  years  after  the  alleged  events,  it  is  wildly  extra- 
vagant. It  does  injustice  to  the  Mythopceic  Faculty 
of  man.  The  period  of  time  that  suffices  for  the 
creation  of  a  full-blown  myth,  must  be  measured  by 
hours  rather  than  by  years.  I  will  give  an  instance 
from  my  own  observation,  if  that  has  not  been  entirely 
discredited  by  my  previous  confessions.  The  bazaars 
of  the  East  are  generally  supposed  to  be  the  peculiar 
home  of  myth,  hotbeds  in  which  myths  grow  with  the 
most  amazing  speed,  but  the  locality  of  my  myth  is 
Aberdeen.  In  the  summer  of  1887  our  town  set  up  in 
one  of  its  steeples  a  very  fine  carillon  of  Belgian  bells. 
There  was  much  public  excitement  over  the  event :  the 
descriptions  of  enthusiastic  promoters  had  prepared  us 
to  hear  silvery  music  floating  all  over  the  town  and 
filling  the  whole  air.  On  the  day  fixed  for  the  in- 
auguration, four  hours  after  the  time  announced  for 


292         Inductive  Logic,  or  the  Logic  of  Science. 

the  first  ceremonial  peal,  not  having  heard  the  bells,  1 
was  in  a  shop  smd  asked  if  anything  had  happened  to 
put  off  the  ceremony.  "Yes,"  I  was  told;  "there  had 
been  an  accident ;  they  had  not  been  properly  hung, 
and  when  the  wife  of  the  Lord  Provost  had  taken  hold 
of  a  string  to  give  the  first  pull,  the  whole  machinery 
had  come  down."  As  a  matter  of  fact  all  that  had 
happened  was  that  the  sound  of  the  bells  was  faint, 
barely  audible  a  hundred  yards  from  the  belfry,  and  not 
at  all  like  what  had  been  expected.  There  were 
hundreds  of  people  in  the  streets,  and  the  myth  had 
originated  somehow  among  those  who  had  not  heard 
what  they  went  out  to  hear.  The  shop  where  it  was 
repeated  circumstantially  to  me  was  in  the  main  street, 
not  more  than  a  quarter  of  a  mile  from  where  the 
carillon  had  been  played  in  the  hearing  of  a  large  but 
disappointed  crowd.  I  could  not  help  reflecting  that  if 
I  had  been  a  mediaeval  chronicler,  I  should  have  gone 
home  and  recorded  the  story,  which  continued  to 
circulate  for  some  days  in  spite  of  the  newspapers  : 
and  two  hundred  years  hence  no  historian  would  have 
ventured  to  challenge  the  truth  of  the  contemporary 
evidence. 


III. — METHOD  OF  TESTING  TRADITIONAL    EVIDENCE. 

It  is  obvious  that  the  tests  applied  to  descriptive 
testimony  in  Courts  of  Law  cannot  be  applied  to  the 
assertions  of  History.  It  is  a  supreme  canon  of 
historical  evidence  that  only  the  statements  of  con- 
temporaries can  be  admitted :  but  most  even  of  their 
statements  must  rest  on  hearsay,  and  even  when  the 
historian  professes  to  have  been  an  eye-witness,  the 
range  of  his  observation  is  necessarily  limited,  and  he 


Ascertainment  of  Simple  Facts  in  their  Order.   293 

cannot  be  put  into  the  witness-box  and  cross-examined. 
Is  there  then  no  way  of  ascertaining  historical  fact  ? 
Must  we  reject  history  as  altogether  unworthy  of 
credit  ? 

The  rational  conclusion  only  is  that  very  few  facts 
can  be  established  by  descriptive  testimony  such  as 
would  satisfy  a  Court  of  Law.  Those  who  look  for 
such  ascertainment  are  on  a  wrong  track,  and  are 
doomed  to  disappointment.  It  is  told  of  Sir  Walter 
Raleigh  that  when  he  was  writing  his  History  of  the 
World,  he  heard  from  his  prison  in  the  Tower  a 
quarrel  outside,  tried  to  find  out  the  rights  and  the 
wrongs  and  the  course  of  it,  and  failing  to  satisfy 
himself  after  careful  inquiry,  asked  in  despair  how  he 
could  pretend  to  write  the  history  of  the  world  when  he 
could  not  find  out  the  truth  about  what  occurred  under 
his  own  windows.  But  this  was  really  to  set  up  an 
impossible  standard  of  historical  evidence. 

The  method  of  testing  historical  evidence  follows 
rather  the  lines  of  the  Newtonian  method  of  Explana- 
tion, which  we  shall  afterwards  describe.  We  must 
treat  any  historical  record  as  being  itself  in  the  first 
place  a  fact  to  be  explained.  The  statement  at  least  is 
extant :  our  first  question  is,  What  is  the  most  rational 
way  of  accounting  for  it  ?  Can  it  be  accounted  for 
most  probably  by  supposing  the  event  stated  to  have 
really  occurred  with  all  the  circumstances  alleged  ?  Or 
is  it  a  more  probable  hypothesis  that  it  was  the  result 
of  an  illusion  of  memory  on  the  part  of  the  original 
observer,  if  it  professes  to  be  the  record  of  an  eye- 
witness, or  on  the  part  of  some  intermediate  trans- 
mitter, if  it  is  the  record  of  a  tradition  ?  To  qualify 
ourselves  to  answer  the  latter  kind  of  question  with 
reasonable  probability  we  must  acquaint  ourselves 


294         Inductive  Logic,  or  the  Logic  of  Science. 

with  the  various  tendencies  to  error  in  personal 
observation  and  in  tradition,  and  examine  how  far  any 
of  them  are  likely  to  have  operated  in  the  given  case. 
We  must  study  the  operation  of  these  tendencies 
within  our  experience,  and  apply  the  knowledge  thus 
gained.  We  must  learn  from  actual  observation  of 
facts  what  the  Mythopceic  Faculty  is  capable  of  in 
the  way  of  creation  and  transmutation,  and  what 
feats  are  beyond  its  powers,  and  then  determine  with 
as  near  a  probability  as  we  can  how  far  it  has  been 
active  in  the  particular  case  before  us. 


CHAPTER  III. 
ASCERTAINMENT  OF  FACTS  OF  CAUSATION, 

I. — POST  Hoc  ERGO  PROPTER  Hoc. 

ONE  of  the  chief  contributions  of  the  Old  Logic  to 
Inductive  Method  was  a  name  for  a  whole  important 
class  of  misobservations.  The  fallacy  entitled  Post 
Hoc  ergo  PropterHoc—"  After,  therefore,  Because  of  " — 
consisted  in  alleging  mere  sequence  as  a  proof  of 
consequence  or  causal  sequence.  The  sophist  appeals 
to  experience,  to  observed  facts :  the  sequence  which 
he  alleges  has  been  observed.  But  the  appeal  is 
fallacious  :  the  observation  on  which  he  relies  amounts 
only  to  this,  that  the  one  event  has  followed  upon  the 
other.  This  much  must  be  observable  in  all  cases  of 
causal  sequence,  but  it  is  not  enough  for  proof.  Post 
hoc  ergo  propter  hoc  may  be  taken  as  a  generic  name  for 
imperfect  proof  of  causation  from  observed  facts  of 
succession. 

The  standard  example  of  the  fallacy  is  the  old 
Kentish  peasant's  argument  that  Tenterden  Steeple 
was  the  cause  of  Goodwin  Sands.  Sir  Thomas  More 
(as  Latimer  tells  the  story  in  one  of  his  Sermons  to 
ridicule  incautious  inference)  had  been  sent  down  into 
Kent  as  a  commissioner  to  inquire  into  the  cause  of 
the  silting  up  of  Sandwich  Haven.  Among  those  who 
came  to  his  court  was  the  oldest  inhabitant,  and 
(295) 


296         Inductive  Logic,  or  the  Logic  of  Science. 

thinking  that  he  from  his  great  age  must  at  least  have 
seen  more  than  anybody  else,  More  asked  him  what 
he  had  to  say  as  to  the  cause  of  the  sands.  "  For- 
sooth, sir,"  was  the  greybeard's  answer,  "  I  am  an  old 
man :  I  think  that  Tenterden  Steeple  is  the  cause  of 
Goodwin  Sands.  For  I  am  an  old  man,  and  I  may 
remember  the  building  of  Tenterden  Steeple,  and  I 
may  remember  when  there  was  no  steeple  at  all  there. 
And  before  that  Tenterden  Steeple  was  in  building, 
there  was  no  manner  of  speaking  of  any  flats  or  sands 
that  stopped  the  haven ;  and,  therefore,  I  think  that 
Tenterden  Steeple  is  the  cause  of  the  destroying  and 
decaying  of  Sandwich  Haven." 

This  must  be  taken  as  Latimer  meant  it  to  be,  a 
ridiculous  example  of  a  purely  imbecile  argument  from 
observation,  but  the  appeal  to  experience  may  have 
more  show  of  reason  and  yet  be  equally  fallacious. 
The  believers  in  Kenelm  Digby's  "Ointment  of 
Honour"  appealed  to  experience  in  support  of  its 
efficacy.  The  treatment  was  to  apply  the  ointment, 
not  to  the  wound,  but  to  the  sword  that  had  inflicted 
it,  to  dress  this  carefully  at  regular  intervals,  and, 
meantime,  having  bound  up  the  wound,  to  leave  it 
alone  for  seven  days.  It  was  observed  that  many  cures 
followed  upon  this  treatment.  But  those  who  inferred 
that  the  cure  was  due  to  the  bandaging  of  the  sword, 
failed  to  observe  that  there  was  another  circumstance 
that  might  have  been  instrumental,  namely,  the 
exclusion  of  the  air  and  the  leaving  of  the  wound 
undisturbed  while  the  natural  healing  processes  went 
on.  And  it  was  found  upon  further  observation  that 
binding  up  the  wound  alone  answered  the  purpose 
equally  well  whether  the  sword  was  dressed  or  not. 

In  cases  where  post  hoc  is  mistaken  for  prcpter  hoc, 


Ascertainment  of  Facts  of  Causation.  297 

simple  sequence  for  causal  sequence,  there  is  com- 
monly some  bias  of  prejudice  or  custom  which  fixes 
observation  on  some  one  antecedent  and  diverts 
attention  from  other  circumstances  and  from  what 
may  be  observed  to  follow  in  other  cases.  In  the 
minds  of  Digby  and  his  followers  there  was  probably 
a  veneration  for  the  sword  as  the  weapon  of  honour, 
and  a  superstitious  belief  in  some  secret  sympathy 
between  the  sword  and  its  owner.  So  when  the 
practice  of  poisoning  was  common,  and  suspicion  was 
flurried  by  panic  fear,  observation  was  often  at  fault. 
Pope  Clement  VIII.  was  said  to  have  been  killed  by 
the  fumes  of  a  poisoned  candle  which  was  placed  in 
his  bedroom.  Undoubtedly  candles  were  there,  but 
those  who  attributed  the  Pope's  death  to  them  took  no 
notice  of  the  fact  that  a  brazier  of  burning  charcoal  was 
at  the  same  time  in  the  apartment  with  no  sufficient 
outlet  for  its  fumes.  Prince  Eugene  is  said  to  have 
received  a  poisoned  letter,  which  he  suspected  and  im- 
mediately threw  from  him.  To  ascertain  whether  his 
suspicions  were  well  founded  the  letter  was  administered 
to  a  dog,  which,  to  make  assurance  doubly  sure,  was 
fortified  by  an  antidote.  The  dog  died,  but  no  inquiry 
seems  to  have  been  made  into  the  character  of  the 
antidote. 

Hotspur's  retort  to  Glendower  showed  a  sound  sense 
of  the  true  value  to  be  attached  to  mere  priority. 

Glendower.  At  my  nativity 

The  front  of  heaven  was  full  of  fiery  shapes, 
Of  burning  cressets :  and  at  my  birth 
The  frame  and  huge  foundation  of  the  earth 
Shaked  like  a  coward. 

Hotspur.  Why  so  it  would  have  done  at  the  same  season,  if 
your  mother's  cat  had  but  kiltened,  though  yourself  had  never 
been  born.  t  Hen.  IV.,  3,  i,  13. 


298         Inductive  Logic,  or  the  Logic  of  Science. 

We  all  admit  at  once  that  the  retort  was  just. 
What  principle  of  sound  conclusion  was  involved  in 
it  ?  It  is  the  business  of  Inductive  Logic  to  make  such 
principles  explicit. 

Taking  Post  Hoc  ergo  Propter  Hoc  as  a  generic  name 
for  fallacious  arguments  of  causation  based  on 
observed  facts,  for  the  fallacious  proof  of  causation 
from  experience,  the  question  for  Logic  is,  What  more 
than  mere  sequence  is  required  to  prove  consequence  ? 
When  do  observations  of  Post  Hoc  warrant  the  con- 
clusion Propter  Hoc? 

II. — MEANING  OF  "CAUSE". — METHODS  OF  OBSERVA- 
TION.—  MILL'S  EXPERIMENTAL  METHODS. 

The  methods  formulated  by  Mill  under  the  name  of 
Experimental  Methods  are  methods  actually  practised 
by  men  of  science  with  satisfactory  results,  and  are 
perfectly  sound  in  principle.  They  were,  indeed,  in 
substance,  taken  by  him  from  the  practice  of  the 
scientific  laboratory  and  study  as  generalised  by 
Herschel.  In  effect  what  Mill  did  was  to  restate  them 
and  fit  them  into  a  system.  But  the  controversies 
into  which  he  was  tempted  in  so  doing  have  somewhat 
obscured  their  exact  function  in  scientific  inquiry. 
Hostile  critics,  finding  that  they  did  not  serve  the  ends 
that  he  seemed  to  claim  for  them,  have  jumped  to  the 
conclusion  that  they  are  altogether  illusory  and  serve 
no  purpose  at  all. 

First,  we  must  dismiss  the  notion,  encouraged  by 
Mill's  general  theory  of  Inference,  that  the  Experi- 
mental Methods  have  anything  special  to  do  with  the 
observation  and  inferential  extension  of  uniformities 
such  as  that  death  is  common  to  all  organised  beings. 


Ascertainment  oj  Facts  oj  Causation.  299 

One  of  the  Methods,  as  we  shall  see,  that  named  by 
Mill  the  Method  of  Agreement,  does  incidentally  and 
collaterally  establish  empirical  laws  in  the  course  of 
its  observations,  and  this  probably  accounts  for  the 
prominence  given  to  it  in  Mill's  system.  But  this  is 
not  its  end  and  aim,  and  the  leading  Method,  that 
named  by  him  the  Method  of  Difference,  establishes 
as  fact  only  a  particular  case  of  causal  coincidence. 
It  is  with  the  proof  of  theories  of  causation  that 
the  Experimental  Methods  are  concerned :  they  are 
methods  of  observing  with  a  view  to  such  proof.1 

The  next  point  to  be  made  clear  is  that  the  facts  of 
causation  with  which  the  Methods  are  concerned  are 
observable  facts,  relations  among  phenomena,  but  that 
the  causal  relations  or  conditions  of  which  they  are 
the  proof  are  not  phenomena,  in  the  meaning  of  being 
manifest  to  the  senses,  but  rather  noumena,  inasmuch 
as  they  are  reached  by  reasoning  from  what  is  mani- 
fest. 

Take,  for  example,  what  is  known  as  the  quaquaversus 
principle  in  Hydrostatics,  that  pressure  upon  a  liquid 
is  propagated  equally  in  all  directions.  We  cannot 
observe  this  extension  of  pressure  among  the  liquid 
particles  directly.  It  cannot  be  traced  among  the 
particles  by  any  of  our  senses.  But  we  can  assume 
that  it  is  so,  consider  what  ought  to  be  visible  if  it  is 
so,  and  then  observe  whether  the  visible  facts  are  in 
accordance  with  the  hypothesis.  A  box  can  be  made, 
rilled  with  water,  and  so  fitted  with  pistons  on  top  and 
bottom  and  on  each  of  its  four  sides  that  they  will 


1  This  is  implied,  as  I  have  already  remarked,  in  the  word 
Experimental.  An  experiment  is  a  proof  or  trial :  of  what  ?  Of  a 
theory,  a  conjecture. 


300         Inductive  Logic,  or  the  Logic  of  Science. 

indicate  the  amount  of  pressure  on  them  from  within. 
Let  pressure  then  be  applied  through  a  hole  in  the  top, 
and  the  pistons  show  that  it  has  been  communicated 
to  them  equally.  The  application  of  the  pressure  and 
the  yielding  of  the  pistons  are  observable  facts,  facts 
in  causal  sequence  :  what  happens  among  the  particles 
of  the  liquid  is  not  observed  but  reasonably  conjectured, 
is  not  phenomenal  but  noumenal. 

This  distinction,  necessary  to  an  understanding  of 
the  scope  of  the  Methods,  was  somewhat  obscured  by 
Mill  in  his  preliminary  discussion  of  the  meaning  of 
"  cause  ".  Very  rightly,  though  somewhat  inconsistently 
with  his  first  theory  of  Induction,  he  insists  that  "  the 
notion  of  Cause  being  the  root  of  the  whole  theory  of 
Induction,  it  is  indispensable  that  this  idea  should  at  the 
very  outset  of  our  inquiry  be,  with  the  utmost  practicable 
degree  of  precision,  fixed  and  determined  ".  But  in  this 
determination,  not  content  with  simply  recognising 
that  it  is  with  phenomena  that  the  Experimental 
Methods  primarily  deal,  it  being  indeed  only  phenomena 
that  can  be  the  subjects  of  experimental  management 
and  observation,  he  starts  by  declaring  that  science 
has  not  to  do  with  any  causes  except  such  as  are 
phenomenal — "  when  I  speak  of  the  cause  of  any 
phenomenon,  I  do  not  mean  a  cause  which  is  not  itself 
a  phenomenon  " — and  goes  on  to  define  as  the  only 
correct  meaning  of  cause  "  the  sum  total  of  conditions," 
including  among  them  conditions  which  are  not 
phenomenal,  in  the  sense  of  being  directly  open  to 
observation. 

When  Mill  protested  that  he  had  regard  only  to 
phenomenal  causes,  he  spoke  as  the  partisan  of  a 
philosophical  tradition.  It  would  have  been  well  if 
he  had  acted  upon  his  own  remark  that  the  proper 


Ascertainment  of  Facts  of  Causation.  301 

understanding  of  the  scientific  method  of  investigating 
cause  is  independent  of  metaphysical  analysis  of  what 
cause  means.  Curiously  enough,  this  remark  is  the 
preface  to  an  analysis  of  cause  which  has  but  slight 
relevance  to  science,  and  is  really  the  continuation  of 
a  dispute  begun  by  Hume.  This  is  the  key  to  his  use 
of  the  word  phenomenon  :  it  must  be  interpreted  with 
reference  to  this :  when  he  spoke  of  causes  as 
phenomenal,  he  opposed  the  word  to  "  occult"  in  some 
supposed  metaphysical  sense.1  And  this  irrelevant 
discussion,  into  the  vortex  of  which  he  allowed  himself 
to  be  carried,  obscured  the  fact,  elsewhere  fully  recog- 
nised by  Mill  himself,  that  science  does  attempt  to  get 
beyond  phenomena  at  ultimate  laws  which  are  not 
themselves  phenomena  though  they  bind  phenomena 
together.  The  "  colligation  "  of  the  facts,  to  use 
WhewelFs  phrase,  is  not  a  phenomenon,  but  a 
noumenon. 

The  truth  is  that  a  very  simple  analysis  of  "  cause  " 
is  sufficient  for  the  purposes  of  scientific  inquiry.  It  is 
enough  to  make  sure  that  causal  sequence  or  conse- 
quence shall  not  be  confounded  with  simple  sequence. 
Causal  sequence  is  simple  sequence  and  something 
more,  that  something  more  being  expressed  by  calling 
it  causal.  What  we  call  a  cause  is  not  merely 
antecedent  or  prior  in  time  to  what  we  call  its  effect : 
it  is  so  related  to  the  effect  that  if  it  or  an  equivalent 
event  had  not  happened  the  effect  would  not  have 
happened.  Anything  in  the  absence  of  which  a 

1  If  we  remember,  as  becomes  apparent  on  exact  psychological 
analysis,  that  things  and  their  qualities  are  as  much  noumena  and 
not,  strictly  speaking,  phenomena  as  the  attraction  of  gravity  or 
the  quaquaversus  principle  in  liquid  pressure,  the  prejudice  against 
occultism  is  mitigated. 


302         Inductive  Logic,  or  the  Logic  of  Science. 

phenomenon  would  not  have  come  to  pass  as  it  did 
come  to  pass  is  a  cause  in  the  ordinary  sense.  We 
may  describe  it  as  an  indispensable  antecedent,  with 
this  reservation  (which  will  be  more  fully  understood 
afterwards),  that  if  we  speak  of  a  general  effect,  such 
as  death,  the  antecedents  must  be  taken  with  corre- 
sponding generality. 

It  is  misleading  to  suggest,  as  Mill  does,  by  defining 
cause  as  "the  sum  total  of  conditions" — a  definition 
given  to  back  up  his  conception  of  cause  as  phenomenal 
— that  science  uses  the  word  cause  in  a  different 
meaning  from  that  of  ordinary  speech.  It  is  quite  true 
that  "  the  cause,  philosophically  speaking,  is  the  sum 
total  of  the  conditions,  positive  and  negative,  taken 
together:  the  whole  of  the  contingencies  of  every 
description,  which  being  realised,  the  consequent 
invariably  follows ".  But  this  does  not  imply  any 
discrepancy  between  the  scientific  or  philosophical 
meaning  and  the  ordinary  meaning.  It  is  only  another 
way  of  saying  that  the  business  of  science  or  philosophy 
is  to  furnish  a  complete  explanation  of  an  event,  an 
account  of  all  its  indispensable  antecedents.  The 
plain  man  would  not  refuse  the  name  of  cause  to 
anything  that  science  or  philosophy  could  prove  to 
be  an  indispensable  antecedent,  but  his  interest  in 
explanation  is  more  limited.  It  is  confined  to  what  he 
wants  to  know  for  the  purpose  he  has  in  hand.  Nor 
could  the  man  of  science  consistently  refuse  the  name 
of  cause  to  what  the  plain  man  applies  it  to,  if  it  really 
was  something  in  consequence  of  which  the  event 
took  place.  Only  his  interest  in  explanation  is 
different.  The  indispensable  antecedents  that  he 
wants  to  know  may  not  be  the  same.  Science  or 
philosophy  applies  itself  to  the  satisfaction  of  a  wider 


Ascertainment  of  Facts  of  Causation.  305 

curiosity :  it  wants  to  know  all  the  causes,  the  whole 
why,  the  sum  total  of  conditions.  To  that  end  the 
various  departments  of  science  interest  themselves  in 
various  species  of  conditions.  But  all  understand  the 
word  cause  in  the  ordinary  sense. 

We  must  not  conclude  from  accidental  differences  in 
explanation  or  statement  of  cause,  dependent  on  the 
purpose  in  view,  that  the  word  Cause  is  used  in 
different  senses.  In  answering  a  question  as  to  the 
cause  of  anything,  we  limit  ourselves  to  what  we 
suppose  our  interrogator  to  be  ignorant  of  and  desirous 
of  knowing.  If  asked  why  the  bells  are  ringing,  we 
mention  a  royal  marriage,  or  a  victory,  or  a  church 
meeting,  or  a  factory  dinner  hour,  or  whatever  the 
occasion  may  be.  We  do  not  consider  it  necessary  to 
mention  that  the  bells  are  struck  by  a  clapper.  Our 
hearer  understands  this  without  our  mentioning  it. 
Nor  do  we  consider  it  necessary  to  mention  the 
acoustic  condition,  that  the  vibration  of  the  bells  is 
communicated  to  our  ears  through  the  air,  or  the 
physiological  condition,  that  the  vibrations  in  the 
drums  of  our  ears  are  conveyed  by  a  certain  mechanism 
of  bone  and  tissue  to  the  nerves.  Our  hearer  may  not 
care  to  know  this,  though  quite  prepared  to  admit 
that  these  conditions  are  indispensable  antecedents. 
Similarly,  a  physiographer,  in  stating  the  cause  of  the 
periodical  inundation  of  the  Nile,  would  consider  it 
enough  to  mention  the  melting  of  snow  on  the  moun- 
tains in  the  interior  of  Africa,  without  saying  anything 
of  such  conditions  as  the  laws  of  gravity  or  the  laws  of 
liquefaction  by  heat,  though  he  knows  that  these  con- 
ditions are  also  indispensable.  Death  is  explained  by 
the  doctor  when  referred  to  a  gunshot  wound,  or  a 
poison,  or  a  virulent  disease.  The  Pathologist  may 


304         Inductive  Logic,  or  the  Logic  of  Science. 

inquire  further,  and  the  Moral  Philosopher  further 
still.  But  all  inquiries  into  indispensable  conditions 
are  inquiries  into  cause.  And  all  alike  have  to  be  on 
their  guard  against  mistaking  simple  sequence  for 
consequence. 

To  speak  of  the  sum  total  of  conditions,  as  the 
Cause  in  a  distinctively  scientific  sense,  is  misleading 
in  another  direction.  It  rather  encourages  the  idea 
that  science  investigates  conditions  in  the  lump,  merely 
observing  the  visible  relations  between  sets  of  ante- 
cedents and  their  consequents.  Now  this  is  the  very 
thing  that  science  must  avoid  in  order  to  make  progress. 
It  analyses  the  antecedent  situation,  tries  to  separate 
the  various  coefficients,  and  finds  out  what  they  are 
capable  of  singly.  It  must  recognise  that  some  of  the 
antecedents  of  which  it  is  in  search  are  not  open  to 
observation.  It  is  these,  indeed,  for  the  most  part 
that  constitute  the  special  subject-matter  of  the 
sciences  in  Molar  as  well  as  in  Molecular  Physics. 
For  practical  every-day  purposes,  it  is  chiefly  the 
visible  succession  of  phenomena  that  concerns  us,  and 
we  are  interested  in  the  latent  conditions  only  in  as  far 
as  they  provide  safer  ground  for  inference  regarding 
such  visible  succession.  But  to  reach  the  latent 
conditions  is  the  main  work  of  science. 

It  is,  however,  only  through  observation  of  what  is 
open  to  the  senses  that  science  can  reach  the  under- 
lying conditions,  and,  therefore,  to  understand  its 
methods  we  must  consider  generally  what  is  open  to 
observation  in  causal  succession.  What  can  be 
observed  when  phenomena  follow  one  another  as 
cause  and  effect,  that  is,  when  the  one  happens  in  con- 
sequence of  the  happening  of  the  other  ?  In  Hume's 
theory,  which  Mill  formally  adopted  with  a  modifica- 


Ascertainment  of  Facts  of  Causation.  305 

tion,1  there  is  nothing  observable  but  the  constancy  or 
invariability  of  the  connexion.  When  we  say  that 
Fire  burns,  there  is  nothing  to  be  observed  except  that 
a  certain  sensation  invariably  follows  upon  close 
proximity  to  fire.  But  this  holds  good  only  if  our 
observation  is  arbitrarily  limited  to  the  facts  enounced 
in  the  expression.  If  this  theory  were  sound,  science 
would  be  confined  to  the  observation  of  empirical  laws. 
But  that  there  is  something  wrong  with  it  becomes 
apparent  when  we  reflect  that  it  has  been  ascertained 
beyond  doubt  that  in  many  observed  changes,  and 
presumably  in  all,  there  is  a  transference  of  energy 
from  one  form  to  another.  The  paralogism  really  lies 
in  the  assumption  from  which  Hume  deduced  his 
theory,  namely,  that  every  idea  is  a  copy  of  some 
impression.  As  a  matter  of  fact,  we  have  ideas  that 
are  not  copies  of  any  one  impression,  but  a  binding 
together,  colligation,  or  intellection  of  several  impres- 
sions. Psychological  analysis  shows  us  that  even  when 
we  say  that  things  exist  with  certain  qualities,  we  are 
expressing  not  single  impressions  or  mental  pheno- 
mena, but  supposed  causes  and  conditions  of  such, 
noumena  in  short,  which  connect  our  recollections  of 
many  separate  impressions  and  expectations  of  more. 
The  Experimental  Methods  proceed  on  the  assump- 
tion that  there  is  other  outward  and  visible  evidence 


1  The  modification  was  that  causation  is  not  only  "  invariable  " 
but  also  "  unconditional "  sequence.  This  addition  of  uncon- 
ditionally as  part  of  the  meaning  of  cause,  after  defining  cause 
as  the  sum  total  of  the  conditions,  is  very  much  like  arguing  in  a 
circle.  After  all,  the  only  point  recognised  in  the  theory  as 
observable  is  the  invariability  of  the  sequence.  But  this  is  less 
important  than  the  fact  that  in  his  canons  of  the  Experimental 
Methods  Mill  recognised  that  more  is  observable. 

20 


306         Inductive  Logic,  or  the  Logic  of  Science. 

of  causal  connexion  than  invariability  of  sequence.  In 
the  leading  Method  it  is  assumed  that  when  events 
may  be  observed  to  follow  one  another  in  a  certain 
way,  they  are  in  causal  sequence.  If  we  can  make 
sure  that  an  antecedent  change  is  the  only  change  that 
has  occurred  in  an  antecedent  situation,  we  have  proof 
positive  that  any  immediately  subsequent  change  in 
the  situation  is  a  consequent,  that  the  successive 
changes  are  in  causal  sequence.  Thus  when  Pascal's 
barometer  was  carried  to  the  top  of  Puy  le  Dome,  and 
the  mercury  in  it  fell,  the  experimenters  argued  that 
the  fall  of  the  mercury  was  causally  connected  with 
the  change  of  elevation,  all  the  other  circumstances 
remaining  the  same.  This  is  the  foundation  of  the 
so-called  Method  of  Difference.  To  determine  that  the 
latent  condition  was  a  difference  in  the  weight  of  the 
atmosphere,  needed  other  observations,  calculations 
and  inferences  ;  but  if  it  could  be  shown  that  the 
elevation  was  the  only  antecedent  changed  in  a  single 
instance,  causal  connexion  was  established  between 
this  and  the  phenomenon  of  the  fall  of  the  barometer. 

It  is  obvious  that  in  coming  to  this  conclusion  we 
assume  what  cannot  be  demonstrated  but  must  simply 
be  taken  as  a  working  principle  to  be  confirmed  by  its 
accordance  with  experience,  that  nothing  comes  into 
being  without  some  change  in  the  antecedent  circum- 
stances. This  is  the  assumption  known  as  the  Law  of 
Causation — ex  nihilo  nihilfit. 

Again,  certain  observable  facts  are  taken  as  evidence 
that  there  is  no  causal  connexion.  On  the  assumption 
that  any  antecedent  in  whose  absence  a  phenomenon 
takes  place  is  not  causally  connected  with  it,  we  set 
aside  or  eliminate  various  antecedents  as  fortuitous  or 
non-causal.  This  negative  principle,  as  we  shall  see, 


Ascertainment  of  Facts  of  Causation.  307 

is  the  foundation  of  what  Mill  called  the  Method  of 
Agreement. 

Be  it  remarked,  once  for  all,  that  before  coming  to 
a  conclusion  on  the  Positive  Method  or  Method  of 
Difference,  we  may  often  have  to  make  many  observa- 
tions on  the  Negative  Method.  Thus  Pascal's  experi- 
menters, before  concluding  that  the  change  of  altitude 
was  the  only  influential  change,  tried  the  barometer  in 
exposed  positions  and  in  sheltered,  when  the  wind 
blew  and  when  it  was  calm,  in  rain  and  in  fog,  in 
order  to  prove  that  these  circumstances  were  indifferent. 
We  must  expound  and  illustrate  the  methods  sepa- 
rately, but  every  method  known  to  science  may  have 
in  practice  to  be  employed  in  arriving  at  a  single 
conclusion. 


CHAPTER  IV. 
METHODS  OF  OBSERVATION.— SINGLE  DIFFERENCE. 

I. — THE  PRINCIPLE  OF  SINGLE  DIFFERENCE. — 
MILL'S  "  CANON". 

ON  what  principle  do  we  decide,  in  watching  a  suc- 
cession of  phenomena,  that  they  are  connected  as 
cause  and  effect,  that  one  happened  in  consequence 
of  the  happening  of  another  ?  It  may  be  worded  as 
follows : — 

When  the  addition  of  an  agent  is  followed  by  the 
appearance  or  its  subtraction  by  the  disappearance 
of  a  certain  effect,  no  other  influential  circumstance 
having  been  added  or  subtracted  at  the  same  time 
or  in  the  meantime,  and  no  change  having  occurred 
among  the  original  circumstances,  that  agent  is  a 
cause  of  the  effect. 

On  this  principle  we  would  justify  our  belief  in  the 
causal  properties  of  common  things — that  fire  burns, 
that  food  appeases  hunger,  that  water  quenches  thirst, 
that  a  spark  ignites  gunpowder,  that  taking  off  a  tight 
shoe  relieves  a  pinched  foot.  We  have  observed  the 
effect  following  when  there  was  no  other  change  in  the 
antecedent  circumstances,  when  the  circumstance  to 
which  we  refer  it  was  simply  added  to  or  subtracted 
from  the  prior  situation. 

(308) 


Methods  of  Observation.  309 

Suppose  we  doubt  whether  a  given  agent  is  or  is  not 
capable  of  producing  a  certain  effect  in  certain  circum- 
stances, how  do  we  put  it  to  the  proof?  We  add  it 
singly  or  subtract  it  singly,  taking  care  that  everything 
else  remains  as  before,  and  watch  the  result.  If  we 
wish  to  know  whether  a  spoonful  of  sugar  can  sweeten 
a  cup  of  tea,  we  taste  the  tea  without  the  sugar,  then 
add  the  sugar,  and  taste  again.  The  isolated  introduc- 
tion of  the  agent  is  the  proof,  the  experiment.  If  we 
wish  to  know  whether  a  pain  in  the  foot  is  due  to  a 
tight  lacing,  we  relax  the  lacing  and  make  no  other 
change :  if  the  pain  then  disappears,  we  refer  it  to  the 
lacing  as  the  cause.  The  proof  is  the  disappearance  of 
the  pain  on  the  subtraction  of  the  single  antecedent. 

The  principle  on  which  we  decide  that  there  is  causal 
connexion  is  the  same  whether  we  make  the  experi- 
mental changes  ourselves  or  merely  watch  them  as 
they  occur — the  only  course  open  to  us  with  the  great 
forces  of  nature  which  are  beyond  the  power  of  human 
manipulation.  In  any  case  we  have  proof  of  causation 
when  we  can  make  sure  that  there  was  only  one 
difference  in  the  antecedent  circumstances  correspond- 
ing to  the  difference  of  result. 

Mill's  statement  of  this  principle,  which  he  calls  the 
Canon  of  the  Method  of  Difference,  is  somewhat  more 
abstract,  but  the  proof  relied  upon  is  substantially  the 
same. 


If  an  instance  in  which  the  phenomenon  under 
investigation  occurs,  and  an  instance  in  which  it 
does  not  occur,  have  every  circumstance  in  common 
save  one,  that  one  occurring  only  in  the  former,  the 
circumstance  in  which  alone  the  two  instances  differ 


3io         Inductive  Logic,  or  the  Logic  of  Science. 

is  \the  effect,  or\ 1  the  cause,  or  an  indispensable  part 
of  the  cause,  of  the  phenomenon. 

Mill's  statement  has  the  merit  of  exactness,  but 
oesides  being  too  abstract  to  be  easy  of  application,  the 
canon  is  apt  to  mislead  in  one  respect.  The  wording 
of  it  suggests  that  the  two  instances  required  must  be 
two  separate  sets  of  circumstances,  such  as  may  be 
put  side  by  side  and  compared,  one  exhibiting  the 
phenomenon  and  the  other  not.  Now  in  practice  it  is 
commonly  one  set  of  circumstances  that  we  observe 
with  a  special  circumstance  introduced  or  withdrawn  : 
the  two  instances,  the  data  of  observation,  are  furnished 
by  the  scene  before  and  the  scene  after  the  experimental 
interference.  In  the  case,  for  example,  of  a  man  shot 
in  the  head  and  falling  dead,  death  being  the  phenom- 
enon in  question,  the  instance  where  it  does  not  occur 
is  the  man's  condition  before  he  received  the  wound, 
and  the  instance  where  it  does  occur  is  his  condition 
after,  the  single  circumstance  of  difference  being  the 
wound,  a  difference  produced  by  the  addition  or 
introduction  of  a  new  circumstance.  Again,  take  the 
common  coin  and  feather  experiment,  contrived  to 
show  that  the  resistance  of  the  air  is  the  cause  of  the 


1Prof.  Bain,  who  adopts  Mill's  Canon,  silently  drops  the  words 
within  brackets.  They  seem  to  be  an  inadvertence.  The  "  cir- 
cumstance," in  all  the  examples  that  Mill  gives,  is  an  antecedent 
circumstance.  Herschel's  statement,  of  which  Mill's  is  an  adap- 
tation, runs  as  follows :  "  If  we  can  either  find  produced  by 
nature,  or  produce  designedly  for  ourselves,  two  instances  which 
agree  exactly  in  all  but  one  particular  and  differ  in  that  one,  its 
influence  in  producing  the  phenomenon,  if  it  have  any,  must 
thereby  be  rendered  apparent  ". 


Methods  of  Observation.  311 

feather's  falling  to  the  ground  more  slowly  than  the 
coin.  The  phenomenon  under  investigation  is  the 
retardation  of  the  feather.  When  the  two  are  dropped 
simultaneously  in  the  receiver  of  an  air-pump,  the  air 
being  left  in,  the  feather  flutters  to  the  ground  after 
the  coin.  This  is  the  instance  where  the  phenomenon 
occurs.  Then  the  air  is  pumped  out  of  the  receiver, 
and  the  coin  and  the  feather  being  dropped  at  the 
same  instant  reach  the  ground  together.  This  is  the 
instance  where  the  phenomenon  does  not  occur.  The 
single  circumstance  of  difference  is  the  presence  of  air 
in  the  former  instance,  a  difference  produced  by  the 
subtraction  of  a  circumstance. 

Mill's  Canon  is  framed  so  as  to  suit  equally  whether 
the  significant  difference  is  produced  by  addition  to  or 
subtraction  from  an  existing  sum  of  circumstances. 
But  that  it  is  misleading  in  so  far  as  it  suggests  that  the 
two  instances  must  be  separate  sets  of  circumstances, 
is  shown  by  the  fact  that  it  misled  himself  when  he 
spoke  of  the  application  of  the  method  in  social 
investigations,  such  as  the  effect  of  Protection  on 
national  wealth.  "  In  order,"  he  says,  "  to  apply  to 
the  case  the  most  perfect  of  the  methods  of  experi- 
mental inquiry,  the  Method  of  Difference,  we  require 
to  find  two  instances  which  tally  in  every  particular 
except  the  one  which  is  the  subject  of  inquiry.  We  must 
have  two  nations  alike  in  all  natural  advantages  and 
disadvantages  ;  resembling  each  other  in  every  quality 
physical  and  moral ;  habits,  usages,  laws,  and  institu- 
tions, and  differing  only  in  the  circumstance  that  the 
one  has  a  prohibitory  tariff  and  the  other  has  not."  It 
being  impossible  ever  to  find  two  such  instances,  he 
concluded  that  the  Method  of  Difference  could  not  be 
applied  in  social  inquiries.  But  really  it  is  not  neces- 


312         Inductive  Logic,  or  the  Logic  of  Science. 

sary  in  order  to  have  two  instances  that  we  should 
have  two  different  nations :  tjie  same  nation  before 
and  after  a  new  law  or  institution  fulfils  that  require- 
ment. The  real  difficulty,  as  we  shall  see,  is  to  satisfy 
the  paramount  condition  that  the  two  instances  shall 
differ  in  a  single  circumstance.  Every  new  enactment 
would  be  an  experiment  after  the  Method  of  Difference, 
if  all  circumstances  but  it  remained  the  same  till  its 
results  appeared.  It  is  because  this  seldom  or  never 
occurs  that  decisive  observation  is  difficult  or  impos- 
sible, and  the  simple  method  of  difference  has  to  be 
supplemented  by  other  means. 

To  introduce  or  remove  a  circumstance  singly  is  the 
typical  application  of  the  principle ;  but  it  may  be  em- 
ployed also  to  compare  the  effects  of  different  agents, 
each  added  alone  to  exactly  similar  circumstances.  A 
simple  example  is  seen  in  Mr.  Jamieson's  agricultural 
experiments  to  determine  the  effects  of  different 
manures,  such  as  coprolite  and  superphosphate,  on 
the  growth  of  crops.  Care  is  taken  to  have  all  the 
antecedent  circumstances  as  exactly  alike  as  possible, 
except  as  regards  the  agency  whose  effects  are  to  be 
observed.  A  field  is  chosen  of  uniform  soil  and  even 
exposure  and  divided  into  plots:  it  is  equally  drained 
so  as  to  have  the  same  degree  of  moisture  throughout ; 
the  seed  is  carefully  selected  for  the  whole  sowing. 
Between  the  sowing  and  the  maturing  of  the  crop  all 
parts  of  the  field  are  open  to  the  same  weather.  Each 
plot  may  thus  be  regarded  as  practically  composing 
the  same  set  of  conditions,  and  any  difference  in  the 
product  may  with  reasonable  probability  be  ascribed  to 
the  single  difference  in  the  antecedents,  the  manures 
which  it  is  desired  to  compare. 


Methods  of  Observation.  313 

II. — APPLICATION  OF  THE  PRINCIPLE. 

The  principle  of  referring  a  phenomenon  to  the  only 
immediately  preceding  change  in  antecedent  circum- 
stances that  could  possibly  have  affected  it,  is  so  simple 
and  so  often  employed  by  everybody  every  day,  that 
at  first  we  do  not  see  how  there  can  be  any  difficulty 
about  it  or  any  possibility  of  error.  And  once  we 
understand  how  many  difficulties  there  are  in  reaching 
exact  knowledge  even  on  this  simple  principle,  and 
what  care  has  to  be  taken,  we  are  apt  to  overrate  its 
value,  and  to  imagine  that  it  carries  us  further  than  it 
really  does.  The  scientific  expert  must  know  how  to 
apply  this  principle,  and  a  single  application  of  it  with 
the  proper  precautions  may  take  him  days  or  weeks, 
and  yet  all  that  can  be  made  good  by  it  may  carry  but 
a  little  way  towards  the  knowledge  of  which  he  is  in 
search. 

When  the  circumstances  are  simple  and  the  effect 
follows  at  once,  as  when  hot  water  scalds,  or  a  blow 
with  a  stick  breaks  a  pane  of  glass,  there  can  be  no 
doubt  of  the  causal  connexion  so  far,  though  plenty 
of  room  for  further  inquiry  into  the  why.  But  the 
mere  succession  of  phenomena  may  be  obscure.  We 
may  introduce  more  than  one  agent  without  knowing 
it,  and  if  some  time  elapses  between  the  experimental 
interference  and  the  appearance  of  the  effect,  other 
agents  may  come  in  without  our  knowledge. 

We  must  know  exactly  what  it  is  that  we  introduce 
and  all  the  circumstances  into  which  we  introduce  it. 
We  are  apt  to  ignore  the  presence  of  antecedents  that 
are  really  influential  in  the  result.  A  man  heated  by 
work  in  the  harvest  field  hastily  swallows  a  glass  of 
water,  and  drops  down  dead.  There  is  no  doubt  that 


314         Inductive  Logic,  or  the  Logic  tf  Science. 

the  drinking  of  the  water  was  a  causal  antecedent,  but 
the  influential  circumstance  may  not  have  been  the 
quantity  or  the  quality  of  the  liquid  but  its  temperature, 
and  this  was  introduced  into  the  situation  as  well  as  a 
certain  amount  of  the  liquid  components.  In  making 
tea  we  put  in  so  much  tea  and  so  much  boiling  water. 
But  the  temperature  of  the  pot  is  also  an  influential 
circumstance  in  the  resulting  infusion.  So  in  chemical 
experiments,  where  one  might  expect  the  result  to 
depend  only  upon  the  proportions  of  the  ingredients, 
it  is  found  that  the  quantity  is  also  influential,  the 
degree  of  heat  evolved  entering  as  a  factor  into  the 
result.  Before  we  can  apply  the  principle  of  single 
difference,  we  must  make  sure  that  there  is  really  only 
a  single  difference  between  the  instances  that  we 
bring  into  comparison. 

The  air-pump  was  invented  shortly  before  the  foun- 
dation of  the  Royal  Society,  and  its  members  made 
many  experiments  with  this  new  means  of  isolating 
an  agent  and  thus  discovering  its  potentialities.  For 
example,  live  animals  were  put  into  the  receiver,  and 
the  air  exhausted,  with  the  result  that  they  quickly 
died.  The  absence  of  the  air  being  the  sole  difference, 
it  was  thus  proved  to  be  indispensable  to  life.  But  air 
is  a  composite  agent,  and  when  means  were  contrived 
of  separating  its  components,  the  effects  of  oxygen 
alone  and  of  carbonic  acid  alone  were  experimentally 
determined. 

A  good  example  of  the  difficulty  of  excluding  agencies 
other  than  those  we  are  observing,  of  making  sure  that 
none  such  intrude,  is  found  in  the  experiments  that 
have  been  made  in  connexion  with  spontaneous 
generation.  The  question  to  be  decided  is  whether 
life  ever  comes  into  existence  without  the  antecedent 


Methods  of  Observation.  315 

presence  of  living  germs.  '  And  the  method  of  deter- 
mining this  is  to  exclude  all  germs  rigorously  from  a 
compound  of  inorganic  matter,  and  observe  whether 
life  ever  appears.  If  we  could  make  sure  in  any  one  case 
that  no  germs  were  antecedently  present,  we  should 
have  proved  that  in  that  case  at  least  life  was 
spontaneously  generated. 

The  difficulty  here  arises  from  the  subtlety  of  the 
agent  under  observation.  The  notion  that  maggots 
are  spontaneously  generated  in  putrid  meat,  was 
comparatively  easy  to  explode.  It  was  found  that 
when  flies  were  excluded  by  fine  wire-gauze,  the 
maggots  did  not  appear.  But  in  the  case  of  micro- 
scopic organisms  proof  is  not  so  easy.  The  germs  are 
invisible,  and  it  is  difficult  to  make  certain  of  their 
exclusion.  A  French  experimenter,  Pouchet,  thought 
he  had  obtained  indubitable  cases  of  spontaneous 
generation.  He  took  infusions  of  vegetable  matter, 
boiled  them  to  a  pitch  sufficient  to  destroy  all  germs 
of  life,  and  hermetically  sealed  up  the  liquid  in  glass 
flasks.  After  an  interval,  micro-organisms  appeared. 
Doubts  as  to  the  conclusion  that  they  had  been 
spontaneously  generated  turned  upon  two  questions : 
whether  all  germs  in  the  liquid  had  been  destroyed  by 
the  preliminary  boiling,  and  whether  germs  could  have 
found  access  in  the  course  of  the  interval  before  life 
appeared.  At  a  certain  stage  in  Pouchet's  process  he 
had  occasion  to  dip  the  mouths  of  the  flasks  in  mercury. 
It  occurred  to  Pasteur  in  repeating  the  experiments 
that  germs  might  have  found  their  way  in  from  the 
atmospheric  dust  on  the  surface  of  this  mercury.  That 
this  was  so  was  rendered  probable  by  his  finding  that 
when  he  carefully  cleansed  the  surface  of  the  mercury 
no  life  appeared  afterwards  in  his  flasks. 


316         Inductive  Logic,  or  the  Logic  of  Science. 

The  application  of  the  principle  in  human  affairs  is 
rendered  uncertain  by  the  immense  complication  of 
the  phenomena,  the  difficulty  of  experiment,  and  the 
special  liability  of  our  judgments  to  prejudice.  That 
men  and  communities  of  men  are  influenced  by  cir- 
cumstances is  not  to  be  denied,  and  the  influence  of 
circumstances,  if  it  is  to  be  traced  at  all,  must  be 
traced  through  observed  facts.  Observation  of  the 
succession  of  phenomena  must  be  part  at  least  of  any 
method  of  tracing  cause  and  effect.  We  must  watch 
what  follows  upon  the  addition  of  new  agencies  to  a 
previously  existing  sum.  But  we  can  seldom  or  never 
get  a  decisive  observation  from  one  pair  of  instances, 
a  clear  case  of  difference  of  result  preceded  by  a  single 
difference  in  the  antecedents.  The  simple  Method  of 
Experimental  Addition  or  Subtraction  is  practically 
inapplicable.  We  can  do  nothing  with  a  man  analogous 
to  putting  him  into  a  hermetically  sealed  retort.  Any 
man  or  any  community  that  is  the  subject  of  our 
observations  must  be  under  manifold  influences. 
Each  of  them  probably  works  some  fraction  of  the 
total  change  observable,  but  how  are  they  to  be  dis- 
entangled ?  Consider,  for  example,  how  impossible  it 
would  be  to  prove  in  an  individual  case,  on  the  strict 
principle  of  Single  Difference,  that  Evil  communica- 
tions corrupt  good  manners.  Moral  deterioration  may 
be  observed  following  upon  the  introduction  of  an  evil 
companion,  but  how  can  we  make  sure  that  no  other 
degrading  influence  has  operated,  and  that  no  original 
depravity  has  developed  itself  in  the  interval  ?  Yet 
such  propositions  of  moral  causation  can  be  proved 
from  experience  with  reasonable  probability.  Only  it 
must  be  by  more  extended  observations  than  the  strict 
Method  of  Difference  takes  into  account.  The  method 


Methods  of  Observation.  317 

is  to  observe  repeated  coincidences  between  evil  com- 
panionship and  moral  deterioration,  and  to  account  for 
this  in  accordance  with  still  wider  observations  of  the 
interaction  of  human  personalities. 

For  equally  obvious  reasons  the  simple  Method  of 
Difference  is  inapplicable  to  tracing  cause  and  effect 
in  communities.  Every  new  law  or  repeal  of  an  old 
law  is  the  introduction  of  a  new  agency,  but  the  effects 
of  it  are  intermixed  with  the  effects  of  other  agencies 
that  operate  at  the  same  time.  Thus  Professor  Cairnes 
remarks,  concerning  the  introduction  of  a  high  Protec- 
tive Tariff  into  the  United  States  in  1861,  that  before 
its  results  could  appear  in  the  trade  and  manufacture 
of  the  States,  there  occurred  (i)  The  great  Civil  War, 
attended  with  enormous  destruction  of  capital ;  (2) 
Consequent  upon  this  the  creation  of  a  huge  national 
debt,  and  a  great  increase  of  taxation ;  (3)  The  issue 
of  an  inconvertible  paper  currency,  deranging  prices 
and  wages ;  (4)  The  discovery  of  great  mineral 
resources  and  oil-springs ;  (5)  A  great  extension  of 
railway  enterprise.  Obviously  in  such  circumstances 
other  methods  than  the  Method  of  Difference  must  be 
brought  into  play  before  there  can  be  any  satisfactory 
reasoning  on  the  facts  observed.  Still  what  investi- 
gators aim  at  is  the  isolation  of  the  results  of  single 
agencies. 


CHAPTER  V. 

METHODS  OF  OBSERVATION.— ELIMINATION.— 
SINGLE  AGREEMENT. 

I.— THE  PRINCIPLE  OF  ELIMINATION. 

THE  essence  of  what  Mill  calls  the  Method  of  Agree- 
ment is  really  the  elimination1  of  accidental,  casual,  or 
fortuitous  antecedents.  It  is  a  method  employed  when 
we  are  given  an  effect  and  set  to  work  to  discover  the 
cause.  It  is  from  the  effect  that  we  start  and  work 
back.  We  make  a  preliminary  analysis  of  the  antece- 
dents ;  call  the  roll,  as  it  were,  of  all  circumstances 
present  before  the  effect  appeared.  Then  we  proceed 
to  examine  other  instances  of  the  same  effect,  and 
other  instances  of  the  occurrence  of  the  various  ante- 
cedents, and  bring  to  bear  the  principle  that  any 
antecedent  in  the  absence  of  which  the  effect  has 
appeared  or  on  the  presence  of  which  it  has  not 
appeared  may  be  set  aside  as  fortuitous,  as  being  not 

1  Elimination,  or  setting  aside  as  being  of  no  concern,  must  not 
be  confounded  with  the  exclusion  of  agents  practised  in  applying 
the  Method  of  Difference.  We  use  the  word  in  its  ordinary  sense 
of  putting  outside  the  sphere  of  an  argument.  By  a  curious  slip, 
Professor  Bain  follows  Mill  in  applying  the  word  sometimes  to 
the  process  of  singling  out  or  disentangling  a  causal  circumstance. 
This  is  an  inadvertent  departure  from  the  ordinary  usage,  according 
to  which  elimination  means  discarding  from  consideration  as  being 
non-essential. 


Methods  of  Observation.  319 

an  indispensable  antecedent.  This  is  really  the 
guiding  principle  of  the  method  as  a  method  of 
observation. 

Let  the  inquiry,  for  example,  be  into  the  cause  of 
Endemic  Goitre.  Instances  of  the  disease  have  been 
collected  from  the  medical  observations  of  all  countries 
over  many  years.  Why  is  it  endemic  in  some  localities 
and  not  in  others  ?  We  proceed  on  the  assumption 
that  the  cause,  whatever  it  is,  must  be  some  circum- 
stance common  to  all  localities  where  it  is  endemic. 
If  any  such  circumstance  is  obvious  at  once,  we  may 
conclude  on  the  mere  principle  of  repeated  coincidence 
that  there  is  causal  connexion  between  it  and  the 
disease,  and  continue  our  inquiry  into  the  nature  of 
the  connexion.  But  if  no  such  circumstance  is  obvious, 
then  in  the  course  of  our  search  for  it  we  eliminate,  as 
fortuitous,  conditions  that  are  present  in  some  cases  but 
absent  in  others.  One  of  the  earliest  theories  was  that 
endemic  goitre  was  connected  with  the  altitude  and 
configuration  of  the  ground,  some  notorious  centres  of 
it  being  deeply  cleft  mountain  valleys,  with  little  air 
and  wind  and  damp  marshy  soil.  But  wider  observa- 
tion found  it  in  many  valleys  neither  narrower  nor 
deeper  than  others  that  were  exempt,  and  also  in  wide 
exposed  valleys  such  as  the  Aar.  Was  it  due  to  the 
geological  formation  ?  This  also  had  to  be  abandoned, 
for  the  disease  is  often  incident  within  very  narrow 
limits,  occurring  in  some  villages  and  sparing  others 
though  the  geological  formation  is  absolutely  the  same. 
Was  it  due  to  the  character  of  the  drinking-water  ? 
Especially  to  the  presence  of  lime  or  magnesia  ?  This 
theory  was  held  strongly,  and  certain  springs  charac- 
terised as  goitre-springs.  But  the  springs  in  some 
goitre  centres  show  not  a  trace  of  magnesia.  The 


320         Inductive  Logic,  or  the  Logic  of  Science. 

comparative  immunity  ot  coast  regions  suggested  that 
it  might  be  owing  to  a  deficiency  of  iodine  in  the 
drinking-water  and  the  air,  and  many  instances  were 
adduced  in  favour  of  this.  But  further  inquiries  made 
out  the  presence  of  iodine  in  considerable  quantities, 
in  the  air,  the  water,  and  the  vegetation  of  districts 
where  goitre  was  widely  prevalent ;  while  in  Cuba  it  is 
said  that  not  a  trace  of  iodine  is  discoverable  either  in 
the  air  or  the  water,  and  yet  it  is  quite  free  irom  goitre. 
After  a  huge  multiplication  of  instances,  resulting  in 
the  elimination  of  every  local  condition  that  had  been 
suggested  as  a  possible  cause,  Hirsch  came  to  the 
conclusion  that  the  true  cause  must  be  a  morbid  poison, 
and  that  endemic  goitre  has  to  be  reckoned  among  the 
infectious  diseases.1 

On  this  negative  principle,  that  if  a  circumstance 
comes  and  goes  without  bringing  the  phenomenon  in 
its  train,  the  phenomenon  is  causally  independent  of 
it,  common-sense  is  always  at  work  disconnecting 
events  that  are  occasionally  coincident  in  time.  A  bird 
sings  at  our  window,  for  example,  and  the  clock  ticks 
on  the  mantelpiece.  But  the  clock  does  not  begin  to 
tick  when  the  bird  begins  to  sing,  nor  cease  to  tick 
when  the  bird  flies  away.  Accordingly,  if  the  clock 
should  stop  at  any  time,  and  we  wished  to  inquire  into 
the  cause,  and  anybody  were  to  suggest  that  the 
stoppage  of  the  clock  was  caused  by  the  stoppage  of 
a  bird's  song  outside,  we  should  dismiss  the  suggestion 
at  once.  We  should  eliminate  this  circumstance  from 
our  inquiry,  on  the  ground  that  from  other  observations 
we  knew  it  to  be  a  casual  or  fortuitous  concomitant. 


1  Hirsch's  Geographical  and  Historical  Pathology,   Creighton's 
translation,  vol.  ii.  pp.  121-202. 


Methods  of  Observation.  321 

Hotspur's  retort  to  Glendover  (p.  297)  was  based  on 
this  principle.  When  poetic  sentiment  or  superstition 
rejects  a  verdict  of  common-sense  or  science,  it  is 
because  it  imagines  a  causal  connexion  to  exist  that  is 
not  open  to  observation,  as  in  the  case  of  the  grand- 
father's clock  which  stopped  short  never  to  go  again 
when  the  old  man  died. 


II. — THE  PRINCIPLE  OF  SINGLE  AGREEMENT. 

The  procedure  in  Mill's  "Method  of  Agreement" 
consists  in  thus  eliminating  fortuitous  antecedents  or 
concomitants  till  only  one  remains.  We  see  the 
nature  of  the  proof  relied  upon  when  we  ask,  How  far 
must  elimination  be  carried  in  order  to  attain  proof  of 
causal  connexion  ?  The  answer  is  that  we  must  go  on 
till  we  have  eliminated  all  but  one.  We  must  multiply 
instances  of  the  phenomenon,  till  we  have  settled  of  each 
of  the  antecedents  except  one  that  it  is  not  the  cause. 
We  must  have  taken  account  of  all  the  antecedents, 
and  we  must  have  found  in  our  observations  that  all 
but  one  have  been  only  occasionally  present. 

When  all  the  antecedents  of  an  effect  except  one  can  be  absent 
without  the  disappearance  of  the  effect,  that  one  is  causally 
connected  with  the  effect,  due  precautions  being  taken 
that  no  other  circumstances  have  been  present  besides 
those  taken  account  of. 

Mill's  Canon  of  the  Method  of  Agreement  is  sub- 
stantially identical  with  this  : — 

When  two  or  more  instances  of  the  phenomenon  under 
investigation  have  only  one  circumstance  in  common, 
the  circumstance  in  which  alone  all  the  instances 
agree  is  the  cause  (or  effect)  of  the  given  pheno- 
menon. 


322         Inductive  Logic ;  or  the  Logic  of  Science. 

Herschel's  statement,  on  which  this  canon  is 
founded,  runs  as  follows :  "  Any  circumstance  in 
which  all  the  facts  without  exception  agree,  may  be  the 
cause  in  question,  or  if  not,  at  least  a  collateral  effect 
of  the  same  cause :  if  there  be  but  one  such  point  of 
agreement,  the  possibility  becomes  a  certainty  ". 

All  the  instances  examined  must  agree  in  one 
circumstance — hence  the  title  Method  of  Agreement. 
But  it  is  not  in  the  agreement  merely  that  the  proof 
consists,  but  the  agreement  in  one  circumstance  com- 
bined with  difference  in  all  the  other  circumstances, 
when  we  are  certain  that  every  circumstance  has  come 
within  our  observation.  It  is  the  singleness  of  the 
agreement  that  constitutes  the  proof  just  as  it  is  the 
singleness  of  the  difference  in  the  Method  of  Diffe- 
rence.1 

It  has  been  said  that  Mill's  Method  of  Agreement 
amounts  after  all  only  to  an  uncontradicted  Inductio 
per  enumerationem  simplicem,  which  he  himself  stigma- 
tised as  Induction  improperly  so  called.  But  this  is 
not  strictly  correct.  It  is  a  misunderstanding  probably 
caused  by  calling  the  method  that  of  agreement  simply, 
instead  of  calling  it  the  Method  of  Single  Agreement, 
so  as  to  lay  stress  upon  the  process  of  elimination  by 
which  the  singleness  is  established.  It  is  true  that 
in  the  course  of  our  observations  we  do  perform  an 
induction  by  simple  enumeration.  In  eliminating,  we 

1  The  bare  titles  Difference  and  Agreement,  though  they  have 
the  advantage  of  simplicity,  are  apt  to  puzzle  beginners  inasmuch 
as  in  the  Method  of  Difference  the  agreement  among  the  instances 
is  at  a  maximum,  and  the  difference  at  a  minimum,  and  vice  versa 
in  the  Method  of  Agreement.  In  both  Methods  it  is  really  the 
isolation  of  the  connexion  between  antecedent  and  sequent  that 
constitutes  the  proof. 


Methods  of  Observation.  323 

at  the  same  time  generalise.  That  is  to  say,  in 
multiplying  instances  for  the  elimination  of  non-causes, 
we  necessarily  at  the  same  time  multiply  instances 
where  the  true  causal  antecedent,  if  there  is  only  one 
possible,  is  present.  An  antecedent  containing  the 
true  cause  must  always  be  there  when  the  phenomenon 
appears,  and  thus  we  may  establish  by  our  eliminating 
observations  a  uniformity  of  connexion  between  two 
facts. 

Take,  for  example,  Roger  Bacon's  inquiry  into  the 
cause  of  the  colours  of  the  rainbow.  His  first  notion 
seems  to  have  been  to  connect  the  phenomenon  with 
the  substance  crystal,  probably  from  his  thinking  of 
the  crystal  firmament  then  supposed  to  encircle  the 
universe.  He  found  the  rainbow  colours  produced  by 
the  passage  of  light  through  hexagonal  crystals.  But 
on  extending  his  observations,  he  found  that  the 
passage  of  light  through  other  transparent  mediums 
was  also  attended  by  the  phenomenon.  He  found  it 
in  dewdrops,  in  the  spray  of  waterfalls,  in  drops 
shaken  from  the  oar  in  rowing.  He  thus  eliminated 
the  substance  crystal,  and  at  the  same  time  established 
the  empirical  law  that  the  passage  of  light  through 
transparent  mediums  of  a  globular  or  prismatic  shape 
was  a  causal  antecedent  of  the  rainbow  colours.1 

Ascertainment  of  invariable  antecedents  may  thus 
proceed  side  by  side  with  that  of  variable  antecedents, 
the  use  of  the  elimination  being  simply  to  narrow  the 
scope  of  the  inquiry.  But  the  proof  set  forth  in  Mill's 
Canon  does  not  depend  merely  on  one  antecedent  or 


1  That  rainbows  in  the  sky  are  produced  by  the  passage  of  light 
through  minute  drops  in  the  clouds  was  an  inference  from  this 
observed  uniformity. 


324         Inductive  Logic,  or  the  Logic  of  Science. 

concomitant  being  invariably  present,  but  also  on  the 
assumption  that  all  the  influential  circumstances  have 
been  within  our  observation.  Then  only  can  we  be 
sure  that  the  instances  have  only  one  circumstance  in 
common. 

The  truth  is  that  owing  to  the  difficulty  of  fulfilling 
this  condition,  proof  of  causation  in  accordance  with 
Mill's  Canon  is  practically  all  but  impossible.  It  is 
not  attained  in  any  of  the  examples  commonly  given. 
The  want  of  conclusiveness  is  disguised  by  the  fact 
that  both  elimination  and  positive  observation  of  mere 
agreement  or  uniform  concomitance  are  useful  and 
suggestive  in  the  search  for  causes,  though  they  do  not 
amount  to  complete  proof  such  as  the  Canon  describes. 
Thus  in  the  inquiry  into  the  cause  of  goitre,  the 
elimination  serves  some  purpose  though  the  result  is 
purely  negative.  When  the  inquirer  is  satisfied  that 
goitre  is  not  originated  by  any  directly  observable  local 
conditions,  altitude,  temperature,  climate,  soil,  water, 
social  circumstances,  habits  of  exertion,  his  search  is 
profitably  limited.  And  mere  frequency,  much  more 
constancy  of  concomitance,  raises  a  presumption  of 
causal  connexion,  and  looking  out  for  it  is  valuable  as 
a  mode  of  reconnoitring.  The  first  thing  that  an 
inquirer  naturally  asks  when  confronted  by  numerous 
instances  of  a  phenomenon  is,  What  have  they  in 
common  ?  And  if  he  finds  that  they  have  some  one 
circumstance  invariably  or  even  frequently  present, 
although  he  cannot  prove  that  they  have  no  other 
circumstance  in  common  as  the  Canon  of  Single 
Agreement  requires,  the  presumption  of  causal  con- 
nexion is  strong  enough  to  furnish  good  ground  for 
further  inquiry.  If  an  inquirer  finds  an  illness  with 
marked  symptoms  in  a  number  of  different  households, 


Methods  of  Observation.  325 

and  finds  also  that  all  the  households  get  their  milk 
supply  from  the  same  source,  this  is  not  conclusive 
proof  of  causation,  but  it  is  a  sufficient  presumption 
to  warrant  him  in  examining  whether  there  is  any 
virulent  ingredient  in  the  milk. 

Thus  varying  the  circumstances  so  as  to  bring  out 
a  common  antecedent,  though  it  does  not  end  in  exact 
proof,  may  indicate  causal  connexion  though  it  does 
not  prove  what  the  nature  of  the  connexion  is.  Roger 
Bacon's  observations  indicated  that  the  production  of 
rainbow  colours  was  connected  with  the  passage  of 
light  through  a  transparent  globe  or  prism.  It  was 
reserved  for  Newton  to  prove  by  other  methods  that 
white  light  was  composed  of  rays,  and  that  those  rays 
were  differently  refracted  in  passing  through  the  trans- 
parent medium.  We  have  another  example  of  how  far 
mere  agreement,  revealed  by  varying  the  circumstances, 
carries  us  towards  discovery  of  the  cause,  in  Wells's 
investigation  of  the  cause  of  dew.  Comparing 
the  numerous  instances  of  dew  appearing  without 
visible  fall  of  moisture,  Wells  found  that  they 
all  agreed  in  the  comparative  coldness  of  the  surface 
dewed.  This  was  all  the  agreement  that  he  established 
by  observation ;  he  did  not  carry  observation  to  the 
point  of  determining  that  there  was  absolutely  no  other 
common  circumstance  :  when  he  had  simply  discovered 
or  detected  that  this  circumstance  was  common  to 
dewed  surfaces,  he  tried  next  to  show  by  reasoning 
from  other  known  facts  how  the  coldness  of  the  surface 
affected  the  aqueous  vapour  of  the  neighbouring  air. 
He  did  not  establish  his  Theory  of  Dew  by  the 
Method  of  Agreement:  but  the  observation  of  an  agree- 
ment or  common  feature  in  a  number  of  instances  was 
a  stage  in  the  process  by  which  he  reached  his  theory. 


326         Inductive  Logic ;  or  the  Logic  of  Science. 

III. — MILL'S  "  JOINT  METHOD  OF  AGREEMENT  AND- 
DIFFERENCE  ". 

After  examining  a  variety  of  instances  in  which  an 
effect  appears,  and  finding  that  they  all  agree  in  the 
antecedent  presence  of  some  one  circumstance,  we 
may  proceed  to  examine  instances  otherwise  similar 
(in  part  materia^  as  Prof.  Fowler  puts  it)  where  the 
effect  does  not  appear.  If  these  all  agree  in  the 
absence  of  the  circumstance  that  is  uniformly  present 
with  the  effect,  we  have  corroborative  evidence  that 
there  is  causal  connexion  between  this  circumstance 
and  the  effect. 

The  principle  of  this  method  seems  to  have  been 
suggested  to  Mill  by  Wells's  investigations  into  Dew. 
Wells  exposed  a  number  of  polished  surfaces  of  various 
substances,  and  compared  those  in  which  there  was  a 
copious  deposit  of  dew  with  those  in  which  there  was 
little  or  none.  If  he  could  have  got  two  surfaces,  one 
dewed  and  the  other  not,  identical  in  every  concomi- 
tant but  one,  he  would  have  attained  complete  proof 
on  the  principle  of  Single  Difference.  But  this  being 
impracticable,  he  followed  a  course  which  approxi- 
mated to  the  method  of  eliminating  every  circumstance 
but  one  from  instances  of  dew,  and  every  circumstance 
but  one  in  instances  of  no-dew.  Mill  sums  up  as 
follows  the  results  of  his  experiments :  "  It  appears 
that  the  instances  in  which  much  dew  is  deposited, 
which  are  very  various,  agree  in  this,  and,  so  far  as  we 
are  able  to  observe,  in  this  only,  that  they  either  radiate 
heat  rapidly  or  conduct  it  slowly :  qualities  between 
which  there  is  no  other  circumstance  of  agreement 
than  that  by  virtue  of  either,  the  body  tends  to  lose 
heat  from  the  surface  more  rapidly  than  it  can  be 


Method's  of  Observation.  327 

restored  from  within.  The  instances,  on  the  contrary, 
in  which  no  dew,  or  but  a  small  quantity  of  it,  is 
formed,  and  which  are  also  extremely  various,  agree 
(as  far  as  we  can  observe)  in  nothing  except  in  not  having 
this  same  property.  We  seem  therefore  to  have 
detected  the  characteristic  difference  between  the  sub- 
stances on  which  the  dew  is  produced,  and  those  on 
which  it  is  not  produced.  And  thus  have  been  realised 
the  requisitions  of  what  we  have  termed  the  Indirect 
Method  of  Difference,  or  the  Joint  Method  of  Agree- 
ment and  Difference."  The  Canon  of  this  Method  is 
accordingly  stated  by  Mill  as  follows : — 

If  two  or  more  instances  in  which  the  phenomenon 
occurs  have  only  one  circumstance  in  common, 
while  two  or  more  instances  in  which  it  does  not 
occur  have  nothing  in  common  save  the  absence  of 
that  circumstance  ;  the  circumstance  in  which  alone 
the  two  sets  of  instances  differ,  is  the  effect,  or  the 
cause,  or  an  indispensable  part  of  the  cause,  of  the 
phenomenon. 

In  practice,  however,  this  theoretical  standard  of 
proof  is  never  attained.  What  investigators  really 
proceed  upon  is  the  presumption  afforded,  to  use  Prof. 
Bain's  terms,  by  Agreement  in  Presence  combined 
with  Agreement  in  Absence.  When  it  is  found  that 
all  substances  which  have  a  strong  smell  agree  in 
being  readily  oxidisable,  and  that  the  marsh  gas  or 
carbonetted  hydrogen  which  has  no  smell  is  not 
oxidisable  at  common  temperatures,  the  presumption 
that  oxidation  is  one  of  the  causal  circumstances  in 
smell  is  strengthened,  even  though  we  have  not  suc- 
ceeded in  eliminating  every  circumstance  but  this  one 
from  either  the  positive  or  the  negative  instances.  So 
in  the  following  examples  given  by  Prof.  Fowler  there 


328         Inductive  Logi'c,  or  the  Logic  of  Science. 

is  not  really  a  compliance  with  the  theoretical  require- 
ments of  Mill's  Method :  there  is  only  an  increased 
presumption  from  the  double  agreement.  "  The  Joint 
Method  of  Agreement  and  Difference  (or  the  Indirect 
Method  of  Difference,  or,  as  I  should  prefer  to  call  it, 
the  Double  Method  of  Agreement)  is  being  continually 
employed  by  us  in  the  ordinary  affairs  of  life.  If  when 
I  take  a  particular  kind  of  food,  I  find  that  I  invari- 
ably suffer  from  some  particular  form  of  illness, 
whereas,  when  I  leave  it  off,  I  cease  to  suffer,  I  enter- 
tain a  double  assurance  that  the  food  is  the  cause  of 
my  illness.  I  have  observed  that  a  certain  plant  is 
invariably  plentiful  on  a  particular  soil ;  if,  with  a 
wide  experience,  I  fail  to  find  it  growing  on  any  other 
soil,  I  feel  confirmed  in  my  belief  that  there  is  in  this 
particular  soil  some  chemical  constituent,  or  some 
peculiar  combination  of  chemical  constituents,  which 
is  highly  favourable,  if  not  essential,  to  the  growth  of 
the  plant." 


CHAPTER  VI. 

METHODS  OF  OBSERVATION.— MINOR  METHODS. 
I. — CONCOMITANT  VARIATIONS. 

Whatever  phenomenon  varies  in  any  manner  whenever 
another  phenomenon  varies  in  some  particular  manner, 
is  either  a  cause  or  an  effect  of  that  phenomenon,  or  is 
connected  with  it  through  some  fact  of  causation. 

THIS  simple  principle  is  constantly  applied  by  us  in 
connecting  and  disconnecting  phenomena.  If  we  hear 
a  sound  which  waxes  and  wanes  with  the  rise  and  fall 
of  the  wind,  we  at  once  connect  the  two  phenomena. 
We  may  not  know  what  the  causal  connexion  is,  but 
if  they  uniformly  vary  together,  there  is  at  once  a 
presumption  that  the  one  is  causally  dependent  on  the 
other,  or  that  both  are  effects  of  the  same  cause. 

This  principle  was  employed  by  Wells  in  his 
researches  into  Dew.  Some  bodies  are  worse  con- 
ductors of  heat  than  others,  and  rough  surfaces  radiate 
heat  more  rapidly  than  smooth.  Wells  made  observa- 
tions on  conductors  and  radiators  of  various  degrees, 
and  found  that  the  amount  of  dew  deposited  was 
greater  or  less  according  as  the  objects  conducted  heat 
slowly  or  radiated  heat  rapidly.  He  thus  established 
what  Herschel  called  a  "  scale  of  intensity  "  between 
the  conducting  and  radiating  properties  of  the  bodies 
bedewed,  and  the  amount  of  the  dew  deposit.  The 
(329) 


33°         Inductive  Logic,  or  the  Logic  of  Science. 

explanation  was  that  in  bad  conductors  the  surface 
cools  more  quickly  than  in  good  conductors  because 
heat  is  more  slowly  supplied  from  within.  Similarly 
in  rough  surfaces  there  is  a  more  rapid  cooling  because 
heat  is  given  off  more  quickly.  But  whatever  the 
explanation  might  be,  the  mere  concomitant  variation 
of  the  dew  deposit  with  these  properties  showed  that 
there  was  some  causal  connexion  between  them. 

It  must  be  remembered  that  the  mere  fact  of  con- 
comitant variation  is  only  an  index  that  some  causal 
connexion  exists.  The  nature  of  the  connexion  must 
be  ascertained  by  other  means,  and  may  remain  a 
problem,  one  of  the  uses  of  such  observed  facts  being 
indeed  to  suggest  problems,  for  inquiry.  Thus  a 
remarkable  concomitance  has  been  observed  between 
spots  on  the  sun,  displays  of  Aurora  Borealis,  and 
magnetic  storms.  The  probability  is  that  they  are 
causally  connected,  but  science  has  not  yet  discovered 
how.  Similarly  in  the  various  sciences  properties  are 
arranged  in  scales  of  intensity,  and  any  correspondence 
between  two  scales  becomes  a  subject  for  investigation 
on  the  assumption  that  it  points  to  a  causal  connexion. 
We  shall  see  afterwards  how  in  social  investigations 
concomitant  variations  in  averages  furnish  material 
for  reasoning. 

When  two  variants  can  be  precisely  measured,  the 
ratio  of  their  variation  may  be  ascertained  by  the 
Method  of  Single  Difference.  We  may  change  an 
antecedent  in  degree,  and  watch  the  corresponding 
change  in  the  effect,  taking  care  that  no  other  agent 
influences  the  effect  in  the  meantime.  Often  when  we 
cannot  remove  an  agent  altogether,  we  may  remove  it 
in  a  measurable  amount,  and  observe  the  result.  We 
cannot  remove  friction  altogether,  but  the  more  it  is 


Methods  of  Observation.  331 

diminished,  the  further  will  a  body   travel   under  the 
impulse  of  the  same  force. 

Until  a  concomitant  variation  has  been  fully 
explained,  it  is  merely  an  empirical  law,  and  any 
inference  that  it  extends  at  the  same  rate  beyond  the 
limits  of  observation  must  be  made  with  due  caution. 
"  Parallel  variation,"  says  Professor  Bain,  ''is  some- 
times interrupted  by  critical  points,  as  in  the  expansion 
of  bodies  by  heat,  which  suffers  a  reverse  near  the 
point  of  cooling.  Again,  the  energy  of  a  solution 
does  not  always  follow  the  strength ;  very  dilute 
solutions  occasionally  exercise  a  specific  power  not 
possessed  in  any  degree  by  stronger.  So,  in  the 
animal  body,  food  and  stimulants  operate  proportionally 
up  to  a  certain  point,  at  which  their  further  operation 
is  checked  by  the  peculiarities  in  the  structure  of  the 
living  organs.  .  .  .  We  cannot  always  reason  from 
a  few  steps  in  a  series  to  the  whole  series,  partly 
because  of  the  occurrence  of  critical  points,  and  partly 
from  the  development  at  the  extremes  of  new  and 
unsuspected  powers.  Sir  John  Herschel  remarks  that 
until  very  recently  '  the  formulas  empirically  deduced 
for  the  elasticity  of  steam,  those  for  the  resistance  of 
fluids,  and  on  other  similar  subjects,  have  almost 
invariably  failed  to  support  the  theoretical  structures 
that  have  been  erected  upon  them  '." * 

II. — SINGLE  RESIDUE. 

Subduct  from  any  phenomenon  such  part  as  previous  induction 
has  shown  to  be  the  effect  of  certain  antecedents,  and  the 
residue  of  the  phenomenon  is  the  effect  of  the  remaining 
antecedents. 

"  Complicated  phenomena,  in  which  several  causes 
1  Bain's  Logic,  vol.  ii.  p.  64. 


332         Inductive  Logic,  or  me  J^ogw  of  Science. 

concurring,  opposing,  or  quite  independent  of  each 
other,  operate  at  once,  so  as  to  produce  a  compound 
effect,  may  be  simplified  by  subducting  the  effect  of  all 
the  known  causes,  as  well  as  the  nature  of  the  case 
permits,  either  by  deductive  reasoning  or  by  appeal  to 
experience,  and  thus  leaving  as  it  were  a  residual 
phenomenon  to  be  explained.  It  is  by  this  process,  in 
fact,  that  science,  in  its  present  advanced  state,  is 
chiefly  promoted.  Most  of  the  phenomena  which 
nature  presents  are  very  complicated ;  and  when  the 
effects  of  all  known  causes  are  estimated  with  exact- 
ness, and  subducted,  the  residual  facts  are  constantly 
appearing  in  the  form  of  phenomena  altogether  new, 
and  leading  to  the  most  important  conclusions."  * 

It  is  obvious  that  this  is  not  a  primary  method  of 
observation,  but  a  method  that  may  be  employed  with 
great  effect  to  guide  observation  when  a  considerable 
advance  has  been  made  in  accurate  knowledge  of 
agents  and  their  mode  of  operation.  The  greatest 
triumph  of  the  method,  the  discovery  of  the  planet 
Neptune,  was  won  some  years  after  the  above  passage 
from  Herschel's  Discourse  was  written.  Certain  per- 
turbations were  observed  in  the  movements  of  the 
planet  Uranus  :  that  is  to  say,  its  orbit  was  found  not 
to  correspond  exactly  with  what  it  should  be  when 
calculated  according  to  the  known  influences  of  the 
bodies  then  known  to  astronomers.  These  perturba- 
tions were  a  residual  phenomenon.  It  was  supposed 
that  they  might  be  due  to  the  action  of  an  unknown 
planet,  and  two  astronomers,  Adams  and  Le  Verrier, 
simultaneously  calculated  the  position  of  a  body  such 
as  would  account  for  the  observed  deviations.  When 

1  Herschel's  Discourse,  §  158. 


Methods  of  Observation.  333 

telescopes  were  directed  to  the  spot  thus  indicated,  the 
planet  Neptune  was  discovered.  This  was  in  Sep- 
tember, 1846 :  before  its  actual  discovery,  Sir  John 
Herschel  exulted  in  the  prospect  of  it  in  language  that 
strikingly  expresses  the  power  of  the  method.  "We 
see  it,"  he  said,  "  as  Columbus  saw  America  from 
the  shores  of  Spain.  Its  movements  have  been  felt, 
trembling  along  the  far-reaching  line  of  our  analysis, 
with  a  certainty  hardly  inferior  to  that  of  ocular 
demonstration." l 

Many  of  the  new  elements  in  Chemistry  have  been 
discovered  in  this  way.  For  example,  when  distinctive 
spectrums  had  been  observed  for  all  known  substances, 
then  on  the  assumption  that  every  substance  has  a 
distinctive  spectrum,  the  appearance  of  lines  not  refer- 
able to  any  known  substance  indicated  the  existence 
of  hitherto  undiscovered  substances  and  directed  search 
for  them.  Thus  Bunsen  in  1860  discovered  two  new 
alkaline  metals,  Caesium  and  Rubidium.  He  was 
examining  alkalies  left  from  the  evaporation  of  a  large 
quantity  of  mineral  water  from  Durkheim.  On  apply- 
ing the  spectroscope  to  the  flame  which  this  particular 
salt  or  mixture  of  salts  gave  off,  he  found  that  some 
bright  lines  were  visible  which  he  had  never  observed 
before,  and  which  he  knew  were  not  produced  either 
by  potash  or  soda.  He  then  set  to  work  to  analyse 
the  mixture,  and  ultimately  succeeded  in  separating 
two  new  alkaline  substances.  When  he  had  succeeded 
in  getting  them  separate,  it  was  of  course  by  the 
Method  of  Difference  that  he  ascertained  them  to  be 
capable  of  producing  the  lines  that  had  excited  his 
curiosity. 

*De  Morgan's  Budget  of  Paradoxes,  p.  237. 


CHAPTER  VII. 
THE  METHOD  OF  EXPLANATION. 

GIVEN  perplexity  as  to  the  cause  of  any  phenomenon, 
what  is  our  natural  first  step  ?  We  may  describe  it  as 
searching  for  a  clue  :  we  look  carefully  at  the  circum- 
stances with  a  view  to  finding  some  means  of  assimi- 
lating what  perplexes  us  to  what  is  already  within  our 
knowledge.  Our  next  step  is  to  make  a  guess,  or 
conjecture,  or,  in  scientific  language,  a  hypothesis. 
We  exercise  our  Reason  or  JVous,  or  Imagination,  or 
whatever  we  choose  to  call  the  faculty,  and  try  to 
conceive  some  cause  that  strikes  us  as  sufficient  to 
account  for  the  phenomenon.  If  it  is  not  at  once 
manifest  that  this  cause  has  really  operated,  our  third 
step  is  to  consider  what  appearances  ought  to  present 
themselves  if  it  did  operate.  We  then  return  to  the 
facts  in  question,  and  observe  whether  those  appear- 
ances do  present  themselves.  If  they  do,  and  if  there 
is  no  other  way  of  accounting  for  the  effect  in  all  its 
circumstances,  we  conclude  that  our  guess  is  correct, 
that  our  hypothesis  is  proved,  that  we  have  reached  a 
satisfactory  explanation. 

These  four  steps  or  stages  may  be  distinguished  in 
most  protracted  inquiries  into  cause.     They  correspond 
to  the  four  stages  of  what  Mr.  Jevons  calls  the  Induc- 
tive Method  par  excellence,    Preliminary    Observation, 
(334) 


The  Method  of  Explanation.  335 

Hypothesis,  Deduction  and  Verification.  Seeing  that 
the  word  Induction  is  already  an  overloaded  drudge, 
perhaps  it  would  be  better  to  call  these  four  stages  the 
Method  of  Explanation.  The  word  Induction,  if  we 
keep  near  its  original  and  most  established  meaning, 
would  apply  strictly  only  to  the  fourth  stage,  the 
Verification,  the  bringing  in  of  the  facts  to  confirm  our 
hypothesis.  We  might  call  the  method  the  Newtonian 
method,  for  all  four  stages  are  marked  in  the  prolonged 
process  by  which  he  made  good  his  theory  of  Gravitation. 
To  give  the  name  of  Inductive  Method  simply  to  all 
the  four  stages  of  an  orderly  procedure  from  doubt  to  a 
sufficient  explanation  is  to  encourage  a  widespread 
misapprehension.  There  could  be  no  greater  error 
than  to  suppose  that  only  the  senses  are  used  in 
scientific  investigation.  There  is  no  error  that  men  of 
science  are  so  apt  to  resent  in  the  mouths  of  the  non- 
scientific.  Yet  they  have  partly  brought  it  on  them- 
selves by  their  loose  use  of  the  word  Induction,  which 
they  follow  Bacon  in  wresting  from  the  traditional 
meaning  of  Induction,  using  it  to  cover  both  Induction 
or  the  bringing  in  of  facts — an  affair  mainly  of  Obser- 
vation— and  Reasoning,  the  exercise  of  Nous,  the 
process  of  constructing  satisfactory  hypotheses.  In 
reaction  against  the  popular  misconception  which 
Bacon  encouraged,  it  is  fashionable  now  to  speak  of  the 
use  of  Imagination  in  Science.  This  is  well  enough 
polemically.  Imagination  as  commonly  understood  is 
akin  to  the  constructive  faculty  in  Science,  and  it  is 
legitimate  warfare  to  employ  the  familiar  word  of  high 
repute  to  force  general  recognition  of  the  truth.  But 
in  common  usage  Imagination  is  appropriated  to 
creative  genius  in  the  Fine  Arts,  and  to  speak  of 
Imagination  in  Science  is  to  suggest  that  Science 


33 6         Inductive  Logic^  or  the  Logic  of  Science. 

deals  in  fictions,  and  has  discarded  Newton's  declara- 
tion Hypotheses  non  fingo.  In  a  fight  for  popular 
respect,  men  of  science  may  be  right  to  claim  for 
themselves  Imagination ;  but  in  the  interests  of  clear 
understanding,  the  logician  must  deplore  that  they 
should  defend  themselves  from  a  charge  due  to  their 
abuse  of  one  word  by  making  an  equally  unwarrantable 
and  confusing  extension  of  another. 

Call  it  what  we  will,  the  faculty  of  likely  guessing, 
of  making  probable  hypotheses,  of  conceiving  in  all  its 
circumstances  the  past  situation  or  the  latent  and 
supramicroscopical  situation  out  of  which  a  phenome- 
non has  emerged,  is  one  of  the  most  important  of  the 
scientific  man's  special  gifts.  It  is  by  virtue  of  it  that 
the  greatest  advancements  of  knowledge  have  been 
achieved,  the  cardinal  discoveries  in  Molar  and 
Molecular  Physics,  Biology,  Geology,  and  all  depart- 
ments of  Science.  We  must  not  push  the  idea  of 
stages  in  explanatory  method  too  far :  the  right 
explanation  may  be  reached  in  a  flash.  The  idea  of 
stages  is  really  useful  mainly  in  trying  to  make  clear 
the  various  difficulties  in  investigation,  and  the  fact 
that  different  men  of  genius  may  show  different  powers 
in  overcoming  them.  The  right  hypothesis  may  occur 
in  a  moment,  as  if  by  simple  intuition,  but  it  may  be 
tedious  to  prove,  and  the  gifts  that  tell  in  proof,  such 
as  Newton's  immense  mathematical  power  in  calculat- 
ing what  a  hypothesis  implies,  Darwin's  patience  in 
verifying,  Faraday's  ingenuity  in  devising  experiments, 
are  all  great  gifts,  and  may  be  serviceable  at  different 
stages.  But  without  originality  and  fertility  in 
probable  hypothesis,  nothing  can  be  done. 

The  dispute  between  Mill  and  Whewell  as  to  the 
place  and  value  of  hypotheses  in  science  was  in  the 


The  Method  cf  Explanation.  337 

main  a  dispute  about  words.  Mill  did  not  really 
undervalue  hypothesis,  and  he  gave  a  most  luminous 
and  accurate  account  of  the  conditions  of  proof.  But 
here  and  there  he  incautiously  spoke  of  the  "  hypo- 
thetical method  "  (by  which  he  meant  what  we  have 
called  the  method  of  Explanation)  as  if  it  were  a 
defective  kind  of  proof,  a  method  resorted  to  by  science 
when  the  "experimental  methods"  could  not  be 
applied.  Whether  his  language  fairly  bore  this  con- 
struction is  not  worth  arguing,  but  this  was  manifestly 
the  construction  that  Whewell  had  in  his  mind  when 
he  retorted,  as  if  in  defence  of  hypotheses,  that  "  the 
inductive  process  consists  in  framing  successive 
hypotheses,  the  comparison  of  these  with  the  ascer- 
tained facts  of  nature,  and  the  introduction  into  them 
of  such  modifications  as  the  comparison  may  render 
necessary".  This  is  a  very  fair  description  of  the 
whole  method  of  explanation.  There  is  nothing  really 
inconsistent  with  it  in  Mill's  account  of  his  "  hypo- 
thetical method  "  ;  only  he  erred  himself  or  was  the 
cause  of  error  in  others  in  suggesting,  intentionally  or 
unintentionally,  that  the  Experimental  Methods  were 
different  methods  of  proof.  The  "  hypothetical  method," 
as  he  described  it,  consisting  of  Induction,  Ratiocina- 
tion, and  Verification,  really  comprehends  the  principles 
of  all  modes  of  observation,  whether  naturally  or  arti- 
ficially experimental.  We  see  this  at  once  when  we 
ask  how  the  previous  knowledge  is  got  in  accordance 
with  which  hypotheses  are  framed.  The  answer  must 
be,  by  Observation.  However  profound  the  calcula- 
tions, it  must  be  from  observed  laws,  or  supposed 
analogues  of  them,  that  we  start.  And  it  is  always  by 
Observation  that  the  results  of  these  calculations  are 
verified. 


338         Inductive  Logic ;  or  the  J^ogic  of  Science. 

Both  Mill  and  Whewell,  however,  confined  them- 
selves too  exclusively  to  the  great  hypotheses  of  the 
Sciences,  such  as  Gravitation  and  the  Undulatory 
Theory  of  Light.  In  the  consideration  of  scientific 
method,  it  is  a  mistake  to  confine  our  attention  to 
these  great  questions,  which  from  the  multitude  of 
facts  embraced  can  only  be  verified  by  prolonged  and 
intricate  inquiry.  Attempts  at  the  explanation  of  the 
smallest  phenomena  proceed  on  the  same  plan,  and  the 
verification  of  conjectures  about  them  is  subject  to 
the  same  conditions,  and  the  methods  of  investigation 
and  the  conditions  of  verification  can  be  studied  most 
simply  in  the  smaller  cases.  Further,  I  venture  to 
think  it  a  mistake  to  confine  ourselves  to  scientific 
inquiry  in  the  narrow  sense,  meaning  thereby  inquiry 
conducted  within  the  pale  of  the  exact  sciences.  For 
not  merely  the  exact  sciences  but  all  men  in  the 
ordinary  affairs  of  life  must  follow  the  same  methods 
or  at  least  observe  the  same  principles  and  conditions, 
in  any  satisfactory  attempt  to  explain. 

Tares  appear  among  the  wheat.  Good  seed  was 
sown  :  whence,  then,  come  the  tares  ?  "  An  enemy 
has  done  this."  If  an  enemy  has  actually  been 
observed  sowing  the  tares,  his  agency  can  be  proved 
by  descriptive  testimony.  But  if  he  has  not  been  seen 
in  the  act,  we  must  resort  to  what  is  known  in  Courts 
of  Law  as  circumstantial  evidence.  This  is  the 
"hypothetical  method"  of  science.  That  the  tares 
are  the  work  of  an  enemy  is  a  hypothesis  :  we  examine 
all  the  circumstances  of  the  case  in  order  to  prove,  by 
inference  from  our  knowledge  of  similar  cases,  that 
thus,  and  thus  only,  can  those  circumstances  be 
accounted  for.  Similarly,  when  a  question  is  raised  as 
to  the  authorship  of  an  anonymous  book.  We  firut 


The  Method  of  Explanation.  339 

search  for  a  clue  by  carefully  noting  the  diction,  the 
structure  of  the  sentences,  the  character  and  sources  of 
the  illustration,  the  special  tracks  of  thought.  We 
proceed  upon  the  knowledge  that  every  author  has 
characteristic  turns  of  phrase  and  imagery  and 
favourite  veins  of  thought,  and  we  look  out  for  such 
internal  evidence  of  authorship  in  the  work  before  us. 
Special  knowledge  and  acumen  may  enable  us  to 
detect  the  authorship  at  once  from  the  general  resem- 
blance to  known  work.  But  if  we  would  have  clear 
proof,  we  must  show  that  the  resemblance  extends  to 
all  the  details  of  phrase,  structure  and  imagery :  we 
must  show  that  our  hypothesis  of  the  authorship  of 
XYZ  explains  all  the  circumstances.  And  even  this 
is  not  sufficient,  as  many  erroneous  guesses  from 
internal  evidence  may  convince  us.  We  must  estab- 
lish further  that  there  is  no  other  reasonable  way  of 
accounting  for  the  matter  and  manner  of  the  book ;  for 
example,  that  it  is  not  the  work  of  an  imitator.  An 
imitator  may  reproduce  all  the  superficial  peculiarities 
of  an  author  with  such  fidelity  that  the  imitation  can 
hardly  be  distinguished  from  the  original :  thus  few 
can  distinguish  between  Fenton's  work  and  Pope's  in 
the  translation  of  the  Odyssey.  We  must  take  such 
known  facts  into  account  in  deciding  a  hypothesis  of 
authorship.  Such  hypotheses  can  seldom,  be  decided 
on  internal  evidence  alone :  other  circumstantial  evi- 
dence— other  circumstances  that  ought  to  be  discover- 
able if  the  hypothesis  is  correct— must  be  searched  for. 
The  operation  of  causes  that  are  manifest  only  in 
their  effects  must  be  proved  by  the  same  method  as  the 
operation  of  past  causes  that  have  left  only  their  effects 
behind  them.  Whether  light  is  caused  by  a  projection 
of  particles  from  a  luminous  body  or  by  an  agitation 


34°         Inductive  Logic,  or  the  Logic  of  Science. 

communicated  through  an  intervening  medium  cannot 
be  directly  observed.  The  only  proof  open  is  to 
calculate  what  should  occur  on  either  hypothesis,  and 
observe  whether  this  does  occur.  In  such  a  case  there 
is  room  for  the  utmost  calculating  power  and  experi- 
mental ingenuity.  The  mere  making  of  the  general 
hypothesis  or  guess  is  simple  enough,  both  modes  of 
transmitting  influence,  the  projection  of  moving  matter 
and  the  travelling  of  an  undulation  or  wave  movement, 
being  familiar  facts.  But  it  is  not  so  easy  to  calculate 
exactly  how  a  given  impulse  would  travel,  and 
what  phenomena  of  ray  and  shadow,  of  reflection, 
refraction  and  diffraction  ought  to  be  visible  in  its 
progress.  Still,  no  matter  how  intricate  the  calcula- 
tion, its  correspondence  with  what  can  be  observed  is 
the  only  legitimate  proof  of  the  hypothesis. 


II. — OBSTACLES  TO  EXPLANATION. — PLURALITY  OF 
CAUSES  AND  INTERMIXTURE  OF  EFFECTS. 

There  are  two  main  ways  in  which  explanation  may 
be  baffled.  There  may  exist  more  than  one  cause 
singly  capable  of  producing  the  effect  in  question,  and 
we  may  have  no  means  of  determining  which  of  the 
equally  sufficient  causes  has  actually  been  at  work. 
For  all  that  appears  the  tares  in  our  wheat  may  be 
the  effect  of  accident  or  of  malicious  design  :  an 
anonymous  book  may  be  the  work  of  an  original  author 
or  of  an  imitator.  Again,  an  effect  may  be  the  joint 
result  of  several  co-operating  causes,  and  it  may  be 
impossible  to  determine  their  several  potencies.  The 
bitter  article  in  the  Quarterly  may  have  helped  to  kill 
John  Keats,  but  it  co-operated  with  an  enfeebled 


The  Method  of  Explanation.  341 

constitution  and  a  naturally  over-sensitive  temperament, 
and  we  cannot  assign  its  exact  weight  to  each  of  these 
coefficients.  Death  may  be  the  result  of  a  combina- 
tion of  causes ;  organic  disease  co-operating  with 
exposure,  over-fatigue  co-operating  with  the  enfeeble- 
ment  of  the  system  by  disease. 

The  technical  names  for  these  difficulties,  Plurality 
of  Causes  and  Intermixture  of  Effects,  are  apt  to  con- 
fuse without  some  clearing  up.  In  both  kinds  of 
difficulty  more  causes  than  one  are  involved :  but  in 
the  one  kind  of  case  there  is  a  plurality  of  possible  or 
equally  probable  causes,  and  we  are  at  a  loss  to  decide 
which :  in  the  other  kind  of  case  there  is  a  plurality  of 
co-operating  causes ;  the  effect  is  the  result  or  product 
of  several  causes  working  conjointly,  and  we  are  unable 
to  assign  to  each  its  due  share. 

It  is  with  a  view  to  overcoming  these  difficulties 
that  Science  endeavours  to  isolate  agencies  and  ascer- 
tain what  each  is  capable  of  singly.  Mill  and  Bain 
treat  Plurality  of  Causes  and  Intermixture  of  Effects 
in  connexion  with  the  Experimental  Methods.  It  is 
better,  perhaps,  to  regard  them  simply  as  obstacles  to 
explanation,  and  the  Experimental  Methods  as  methods 
of  overcoming  those  obstacles.  The  whole  purpose  of 
the  Experimental  Methods  is  to  isolate  agencies  and 
effects  :  unless  they  can  be  isolated,  the  Methods  are 
inapplicable.  In  situations  where  the  effects  observable 
may  be  referred  with  equal  probability  to  more  than 
one  cause,  you  cannot  eliminate  so  as  to  obtain  a 
single  agreement.  The  Method  of  Agreement  is 
frustrated.  And  an  investigator  can  get  no  light  from 
mixed  effects,  unless  he  knows  enough  of  the  causes  at 
work  to  be  able  to  apply  the  Method  of  Residues.  If 
he  does  not,  he  must  simply  look  out  for  or  devise 


342         Inductive  Logic ;  or  the  Logic  of  Science, 

instances  where  the  agencies  are  at  work  separately, 
and  apply  the  principle  of  Single  Difference. 

Great,  however,  as  the  difficulties  are,  the  theory  of 
Plurality  and  Intermixture  baldly  stated  makes  them 
appear  greater  than  they  are  in  practice.  There  is  a 
consideration  that  mitigates  the  complication,  and 
renders  the  task  of  unravelling  it  not  altogether 
hopeless.  This  is  that  different  causes  have  distinctive 
ways  of  operating,  and  leave  behind  them  marks  of 
their  presence  by  which  their  agency  in  a  given  case 
may  be  recognised. 

An  explosion,  for  example,  occurs.  There  are 
several  explosive  agencies,  capable  of  causing  as  much 
destruction  as  meets  the  eye  at  the  first  glance.  The 
agent  in  the  case  before  us  may  be  gunpowder  or  it 
may  be  dynamite.  But  the  two  agents  are  not  so 
alike  in  their  mode  of  operation  as  to  produce  results 
identical  in  every  circumstance.  The  expert  inquirer 
knows  by  previous  observation  that  when  gunpowder 
acts  the  objects  in  the  neighbourhood  are  blackened  ; 
and  that  an  explosion  of  dynamite  tears  and  shatters  in 
a  way  peculiar  to  itself.  He  is  thus  able  to  interpret 
the  traces,  to  make  and  prove  a  hypothesis. 

A  man's  body  is  found  dead  in  water.  It  may  be 
a  question  whether  death  came  by  drowning  or  by 
previous  violence.  He  may  have  been  suffocated  and 
afterwards  thrown  into  the  water.  But  the  circum- 
stances will  tell  the  true  story.  Death  by  drowning 
has  distinctive  symptoms.  If  drowning  was  the  cause, 
water  will  be  found  in  the  stomach  and  froth  in  the 
trachea. 

Thus,  though  there  may  be  a  plurality  of  possible 
causes,  the  causation  in  the  given  case  may  be  brought 
home  to  one  by  distinctive  accompaniments,  and  it  is 


The  Method  of  Explanation.  343 

the  business  of  the  scientific  inquirer  to  study  these. 
What  is  known  as  the  "ripple-mark"  in  sandstone 
surfaces  may  be  produced  in  various  ways.  The  most 
familiar  way  is  by  the  action  of  the  tides  on  the  sand 
of  the  sea-shore,  and  the  interpreter  who  knows  this 
way  only  would  ascribe  the  marks  at  once  to  this 
agency.  But  ripple-marks  are  produced  also  by  the 
winds  on  drifting  sands,  by  currents  of  water  where  no 
tidal  influence  is  felt,  and  in  fact  by  any  body  of  water 
in  a  state  of  oscillation.  Is  it,  then,  impossible  to 
decide  between  these  alternative  possibilities  of 
causation  ?  No  :  wind-ripples  and  current-ripples  and 
tidal-ripples  have  each  their  own  special  character  and 
accompanying  conditions,  and  the  hypothesis  of  one 
rather  than  another  may  be  made  good  by  means  of 
these.  "  In  rock-formations,"  Mr.  Page  says,1  "  there 
are  many  things  which  at  first  sight  seem  similar, 
and  yet  on  more  minute  examination,  differences  are 
detected  and  conditions  discovered  which  render  it 
impossible  that  these  appearances  can  have  arisen 
from  the  same  causation." 

The  truth  is  that  generally  when  we  speak  of 
plurality  of  causes,  of  alternative  possibilities  of  causa- 
tion, we  are  not  thinking  of  the  effect  in  its  individual 
entirety,  but  only  of  some  general  or  abstract  aspect 
of  it.  When  we  say,  e.g.,  that  death  may  be  produced 
by  a  great  many  different  causes,  poison,  gunshot 
wounds,  disease  of  this  or  that  organ,  we  are  thinking 
of  death  in  the  abstract,  not  of  the  particular  case 
under  consideration,  which  as  an  individual  case,  has 
characters  so  distinctive  that  only  one  combination  of 
causes  is  possible. 

1  Page's  Philosophy  of  Geology,  p.  38. 


344         Inductive  Logic,  or  the  Logic  of  Science. 

The  effort  of  science  is  to  become  less  and  less 
abstract  in  this  sense,  by  observing  agencies  or  com- 
binations of  agencies  apart  and  studying  the  special 
characters  of  their  effects.  That  knowledge  is  then 
applied,  on  the  assumption  that  where  those  characters 
are  present,  the  agent  or  combination  of  agencies  has 
been  at  work  Given  an  effect  to  be  explained,  it  is 
brought  home  to  one  out  of  several  possible  alternatives 
by  circumstantial  evidence. 

Bacon's  phrase,  Instantia  Crucis?  or  Finger-post 
Instance,  might  be  conveniently  appropriated  as  a 
technical  name  for  a  circumstance  that  is  decisive 
between  rival  hypotheses.  This  was,  in  effect,  pro- 
posed by  Sir  John  Herschel,2  who  drew  attention  to 
the  importance  of  these  crucial  instances,  and  gave  the 
following  example :  "  A  curious  example  is  given  by 
M.  Fresnel,  as  decisive,  in  his  mind,  of  the  question 
between  the  two  great  opinions  on  the  nature  of  light, 
which,  since  the  time  of  Newton  and  Huyghens,  have 
divided  philosophers.  When  two  very  clean  glasses 
are  laid  one  on  the  other,  if  they  be  not  perfectly  flat, 
but  one  or  both  in  an  almost  imperceptible  degree 
convex  or  prominent,  beautiful  and  vivid  colours  will 
be  seen  between  them  ;  and  if  these  be  viewed  through 
a  red  glass,  their  appearance  will  be  that  of  alternate 
dark  and  bright  stripes.  .  .  .  Now,  the  coloured  stripes 
thus  produced  are  explicable  on  both  theories,  and  are 
appealed  to  by  both  as  strong  confirmatory  facts ;  but 
there  is  a  difference  in  one  circumstance  according  as 
one  or  the  other  theory  is  employed  to  explain  them. 
In  the  case  of  the  Huyghenian  doctrine,  the  intervals 

1  Crux  in  this  phrase  means  a  cross  erected  at  the  parting  of 
ways,  with  arms  to  tell  whither  each  way  leads. 

2  Discourse,  §  218. 


The  Method  of  Explanation.  345 

between  the  bright  stripes  ought  to  appear  absolutely 
black;  in  the  other,  half  bright,  when  viewed  [in  a 
particular  manner]  through  a  prism.  This  curious 
case  of  difference  was  tried  as  soon  as  the  opposing 
consequences  of  the  two  theories  were  noted  by  M. 
Fresnel,  and  the  result  is  stated  by  him  to  be  decisive 
in  favour  of  that  theory  which  makes  light  to  consist 
in  the  vibrations  of  an  elastic  medium." 


III. — THE  PROOF  OF  A  HYPOTHESIS. 

The  completest  proof  of  a  hypothesis  is  when  that 
which  has  been  hypothetically  assumed  to  exist  as  a 
means  of  accounting  for  certain  phenomena  is  after- 
wards actually  observed  to  exist  or  is  proved  by 
descriptive  testimony  to  have  existed.  Our  argument, 
for  example,  from  internal  evidence  that  Mill  in  writing 
his  Logic  aimed  at  furnishing  a  method  for  social 
investigations  is  confirmed  by  a  letter  to  Miss  Caroline 
Fox,  in  which  he  distinctly  avowed  that  object. 

The  most  striking  example  of  this  crowning  verifi- 
cation in  Science  is  the  discovery  of  the  planet 
Neptune,  in  which  case  an  agent  hypothetically 
assumed  was  actually  brought  under  the  telescope  as 
calculated.  Examples  almost  equally  striking  have 
occurred  in  the  history  of  the  Evolution  doctrine. 
Hypothetical  ancestors  with  certain  peculiarities  of 
structure  have  been  assumed  as  links  between  living 
species,  and  in  some  cases  their  fossils  have  actually 
been  found  in  the  geological  register. 

Such  triumphs  of  verification  are  necessarily  rare. 
For  the  most  part  the  hypothetical  method  is  applied 
to  cases  where  proof  by  actual  observation  is  impossible, 
such  as  prehistoric  conditions  of  the  earth  or  of  life 


346         Inductive  Logic,  or  the  Logic  of  Science. 

upon  the  earth,  or  conditions  in  the  ultimate  constitu- 
tion of  matter  that  are  beyond  the  reach  of  the  strongest 
microscope.  Indeed,  some  would  confine  the  word 
hypothesis  to  cases  of  this  kind.  This,  in  fact,  was 
done  by  Mill :  hypothesis,  as  he  defined  it,  was  a  con- 
jecture not  completely  proved,  but  with  a  large  amount 
of  evidence  in  its  favour.  But  seeing  that  the  proce- 
dure of  investigation  is  the  same,  namely,  conjecture, 
calculation  and  comparison  of  facts  with  the  calculated 
results,  whether  the  agency  assumed  can  be  brought 
to  the  test  of  direct  observation  or  not,  it  seems  better 
not  to  restrict  the  word  hypothesis  to  incompletely 
proved  conjectures,  but  to  apply  it  simply  to  a  conjec- 
ture made  at  a  certain  stage  in  whatever  way  it  may 
afterwards  be  verified. 

In  the  absence  of  direct  verification,  the  proof  of 
a  hypothesis  is  exclusive  sufficiency  to  explain  the 
circumstances.  The  hypothesis  must  account  for  all 
the  circumstances,  and  there  must  be  no  other  way  of 
accounting  for  them.  Another  requirement  was  men- 
tioned by  Newton  in  a  phrase  about  the  exact  meaning 
of  which  there  has  been  some  contention.  The  first 
of  his  Regulas  Philosophandi  laid  down  that  the  cause 
assumed  must  be  a  vera  causa.  "We  are  not,"  the 
Rule  runs,  "  to  admit  other  causes  of  natural  things 
than  such  as  both  are  true,  and  suffice  for  explaining 
their  phenomena." 1 

It  has  been  argued  that  the  requirement  of  "verity  " 
is  superfluous  ;  that  it  is  really  included  in  the  require- 
ment of  sufficiency ;  that  if  a  cause  is  sufficient  to 
explain  the  phenomena  it  must  ipso  facto  be  the  true 

1  Causas  rerum  naturalium  non  plures  admitti  debere  quam 
quae  et  verae  sint  et  earum  pheriomenis  explicandis  sufficiant. 


The  Method  of  Explanation.  347 

cause.  This  may  be  technically  arguable,  given  a 
sufficient  latitude  to  the  word  sufficiency  :  nevertheless, 
it  is  convenient  to  distinguish  between  mere  sufficiency 
to  explain  the  phenomena  in  question,  and  the  proof 
otherwise  that  the  cause  assigned  really  exists  in  rerum 
natura,  or  that  it  operated  in  the  given  case.  The 
frequency  with  which  the  expression  vera  causa  has 
been  used  since  Newton's  time  shows  that  a  need  is 
felt  for  it,  though  it  may  be  hard  to  define  "  verity  " 
precisely  as  something  apart  from  "sufficiency  ".  If  we 
examine  the  common  usage  of  the  expression  we  shall 
probably  find  that  what  is  meant  by  insisting  on  a  vera 
causa  is  that  we  must  have  some  evidence  for  the  cause 
assigned  outside  the  phenomena  in  question.  In 
seeking  for  verification  of  a  hypothesis  we  must  extend 
our  range  beyond  the  limited  facts  that  have  engaged 
our  curiosity  and  that  demand  explanation. 

There  can  be  little  doubt  that  Newton  himself  aimed 
his  rule  at  the  Cartesian  hypothesis  of  Vortices.  This 
was  an  attempt  to  explain  the  solar  system  on  the 
hypothesis  that  cosmic  space  is  filled  with  a  fluid  in 
which  the  planets  are  carried  round  as  chips  of  wood 
in  a  whirlpool,  or  leaves  or  dust  in  a  whirlwind.  Now 
this  is  so  far  a  vera  causa  that  the  action  of  fluid 
vortices  is  a  familiar  one :  we  have  only  to  stir  a  cup 
of  tea  with  a  bit  of  stalk  in  it  to  get  an  instance.  The 
agency  supposed  is  sufficient  also  to  account  for  the 
revolution  of  a  planet  round  the  sun,  given  sufficient 
strength  in  the  fluid  to  buoy  up  the  planet.  But  if 
there  were  such  a  fluid  in  space  there  would  be  other 
phenomena  :  and  in  the  absence  of  these  other 
phenomena  the  hypothesis  must  be  dismissed  as 
imaginary.  The  fact  that  comets  pass  into  and  out 
of  spaces  where  the  vortices  must  be  assumed  to  be 


348         Inductive  Logic,  or  the  Logic  of  Science. 

in  action  without  exhibiting  any  perturbation  is  an 
instantia  cruets  against  the  hypothesis. 

If  by  the  requirement  of  a  vera  causa  were  meant 
that  the  cause  assigned  must  be  one  directly  open  to 
observation,  this  would  undoubtedly  be  too  narrow  a 
limit.  It  would  exclude  such  causes  as  the  ether  which 
is  assumed  to  fill  interstellar  space  as  a  medium 
for  the  propagation  of  light.  The  only  evidence  for 
such  a  medium  and  its  various  properties  is  sufficiency 
to  explain  the  phenomena.  Like  suppositions  as  to 
the  ultimate  constitution  of  bodies,  it  is  of  the  nature 
of  what  Professor  Bain  calls  a  "  Representative 
Fiction  "  :  the  only  condition  is  that  it  must  explain  all 
the  phenomena,  and  that  there  must  be  no  other  way  of 
explaining  all.  When  it  is  proved  that  light  travels 
with  a  finite  velocity,  we  are  confined  to  two  alternative 
ways  of  conceiving  its  transmission,  a  projection  of 
matter  from  the  luminous  body  and  the  transference  of 
vibrations  through  an  intervening  medium.  Either 
hypothesis  would  explain  many  of  the  facts :  our 
choice  must  rest  with  that  which  best  explains  all. 
But  supposing  that  all  the  phenomena  of  light  were 
explained  by  attributing  certain  properties  to  this 
intervening  medium,  it  would  probably  be  held  that 
the  hypothesis  of  an  ether  had  not  been  fully  verified 
till  other  phenomena  than  those  of  light  had  been 
shown  to  be  incapable  of  explanation  on  any  other 
hypothesis.  If  the  properties  ascribed  to  it  to  explain 
the  phenomena  of  light  sufficed  at  the  same  time  to 
explain  otherwise  inexplicable  phenomena  connected 
with  Heat,  Electricity,  or  Gravity,  the  evidence  of  its 
reality  would  be  greatly  strengthened. 

Not  only  must  the  circumstances  in  hand  be 
explained,  but  other  circumstances  must  be  found  to 


The  Method  of  Explanation.  349 

be  such  as  we  should   expect   if  the  cause   assigned 
really    operated.     Take,    for    example,    the    case    of 
Erratic  blocks   or   boulders,  huge   fragments  of  rock 
found  at  a   distance  from    their   parent    strata.     The 
lowlands  of  England,  Scotland,  and  Ireland,  and  the 
great  central  plain  of  Northern  Europe  contain  many 
such  fragments.     Their  composition  shows  indubitably 
that  they  once  formed  part  of  hills  to  the  northward  of 
their  present  site.     They  must  somehow  have  been 
detached  and  transported  to  where  we  now  find  them. 
How  ?     One  old  explanation  is  that  they  were  carried 
by  witches,  or  that  they  were  themselves  witches  acci- 
dentally dropped  and  turned  into   stone.     Any  such 
explanation    by   supernatural    means   can    neither  be 
proved  nor  disproved.     Some  logicians  would   exclude 
such  hypotheses  altogether  on   the  ground  that  they 
cannot  be  rendered  either  more  or  less  probable  by  subse- 
quent examination.1     The  proper  scientific  limit,  how- 
ever, is  not  to  the  making  of  hypotheses,  but  to  the 
proof  of  them.     The   more  hypotheses  the  merrier  : 
only  if  such  an  agency  as  witchcraft  is  suggested,  we 
should  expect  to  find  other  evidence  of  its  existence  in 
other  phenomena  that  could  not  otherwise  be  explained. 
Again,  it  has  been  suggested  that  the  erratic  boulders 
may  have  been  transported  by  water.     Water  is  so  far 
a  vera  causa  that  currents  are  known  to  be  capable  of 
washing  huge  blocks  to  a  great  distance.     But  blocks 
transported  in  this  way  have  the  edges  worn  off  by  the 
friction  of  their  passage  :  and,  besides,  currents  strong 
enough  to  dislodge  and  force  along  for  miles  blocks 
as  big  as  cottages  must  have  left  other  marks  of  their 


1  See  Prof.  Fowler  on  the  Conditions  of  Hypotheses,  Inductive 
Logic,  pp.  100-115. 


350         Inductive  Logic,  or  the  Logic  of  Science. 

presence.  The  explanation  now  received  is  that 
glaciers  and  icebergs  were  the  means  of  transport. 
But  this  explanation  was  not  accepted  till  multitudes 
of  circumstances  were  examined  all  tending  to  show 
that  glaciers  had  once  been  present  in  the  regions 
where  the  erratic  blocks  are  found.  The  minute  habits 
of  glaciers  have  been  studied  where  they  still  exist : 
how  they  slowly  move  down  carrying  fragments  of 
rock  ;  how  icebergs  break  off  when  they  reach  water, 
float  off  with  their  load,  and  drop  it  when  they  melt ; 
how  they  grind  and  smooth  the  surfaces  of  rocks  over 
which  they  pass  or  that  are  frozen  into  them :  how 
they  undercut  and  mark  the  faces  of  precipices  past 
which  they  move  ;  how  moraines  are  formed  at  the 
melting  ends  of  them,  and  so  forth.  When  a  district 
exhibits  all  the  circumstances  that  are  now  observed 
to  attend  the  action  of  glaciers  the  proof  of  the 
hypothesis  that  glaciers  were  once  there  is  complete. 


CHAPTER  VIII. 

SUPPLEMENTARY  METHODS  OF  INVESTIGATION. 

I. — THE   MAINTENANCE  OF  AVERAGES. — SUPPLEMENT 
TO  THE  METHOD  OF  DIFFERENCE. 

A  CERTAIN  amount  of  law  obtains  among  events  that 
are  usually  spoken  of  as  matters  of  chance  or  accident 
in  the  individual  case.  Every  kind  of  accident  recurs 
with  a  certain  uniformity.  If  we  take  a  succession  of 
periods,  and  divide  the  total  number  of  any  kind  of 
event  by  the  number  of  periods,  we  get  what  is  called 
the  average  for  that  period :  and  it  is  observed  that 
such  averages  are  maintained  from  period  to  period. 
Over  a  series  of  years  there  is  a  fixed  proportion 
between  good  harvests  and  bad,  between  wet  days  and 
dry  :  every  year  nearly  the  same  number  of  suicides 
takes  place,  the  same  number  of  crimes,  of  accidents 
to  life  and  limb,  even  of  suicides,  crimes,  or  injuries  by 
particular  means :  every  year  in  a  town  nearly  the 
same  number  of  children  stray  from  their  parents  and 
are  restored  by  the  police  :  every  year  nearly  the  same 
number  of  persons  post  letters  without  putting  an 
address  on  them. 

This  maintenance  of  averages  is  simple  matter  of 
observation,  a  datum  of  experience,  an  empirical  law. 
Once  an  average  for  any  kind  of  event  has  been 
noted,  we  may  count  upon  its  continuance  as  we  count 
upon  the  continuance  of  any  other  kind  of  observed 
(35*) 


352         Inductive  Logic,  or  the  Logic  of  Science. 

uniformity.  Insurance  companies  proceed  upon  such 
empirical  laws  of  average  in  length  ol  life  and 
immunity  from  injurious  accidents  by  sea  or  land : 
their  prosperity  is  a  practical  proof  of  the  correctness 
and  completeness  of  the  observed  facts  and  the  sound- 
ness of  their  inference  to  the  continuance  of  the  average. 

The  constancy  of  averages  is  thus  a  guide  in  prac- 
tice. But  in  reasoning  upon  them  in  investigations  of 
cause,  we  make  a  further  assumption  than  continued 
uniformity.  We  assume  that  the  maintenance  of  the 
average  is  due  to  the  permanence  of  the  producing 
causes.  We  regard  the  average  as  the  result  of  the 
operation  of  a  limited  sum  of  forces  and  conditions, 
incalculable  as  regards  their  particular  incidence,  but 
always  pressing  into  action,  and  thus  likely  to  operate 
a  certain  number  of  times  within  a  limited  period. 

Assuming  the  correctness  of  this  explanation,  it 
would  follow  that  any  change  in  the  average  is  due  to 
some  change  in  the  producing  conditions  ;  and  this  deriva- 
tive law  is  applied  as  a  help  in  the  observation  and 
explanation  of  social  facts.  Statistics  are  collected 
and  classified  :  averages  are  struck :  and  changes  in 
the  average  are  referred  to  changes  in  the  concomitant 
conditions. 

With  the  help  of  this  law,  we  may  make  a  near 
approach  to  the  precision  of  the  Method  of  Difference. 
A  multitude  of  unknown  or  unmeasured  agents  may 
be  at  work  on  a  situation,  but  we  may  accept  the 
average  as  the  result  of  their  joint  operation.  If  then 
a  new  agency  is  introduced  or  one  of  the  known  agents 
is  changed  in  degree,  and  this  is  at  once  followed  by  a 
change  in  the  average,  we  may  with  fair  probability 
refer  the  change  in  the  result  to  the  change  in  the 
antecedents. 


Supplementary  Methods  of  Investigation.         353 

The  difficulty  is  to  find  a  situation  where  only  one 
antecedent  has  been  changed  before  •  the  appearance 
of  the  effect.  This  difficulty  may  be  diminished  in 
practice  by  eliminating  changes  that  we  have  reason 
to  know  could  not  have  affected  the  circumstances  in 
question.  Suppose,  for  example,  our  question  is 
whether  the  Education  Act  of  1872  had  an  influence 
in  the  decrease  of  juvenile  crime.  Such  a  decrease 
took  place  post  hoc ;  was  it  propter  hoc  ?  We  may  at 
once  eliminate  or  put  out  of  account  the  abolition  of 
Purchase  in  the  Army  or  the  extension  of  the  Franchise 
as  not  having  possibly  exercised  any  influence  on 
juvenile  crime.  But  with  all  such  eliminations,  there 
may  still  remain  other  possible  influences,  such  as  an 
improvement  in  the  organisation  of  the  Police,  or  an 
expansion  or  contraction  of  employment.  "  Can  you 
tell  me  in  the  face  of  chronology,"  a  leading  statesman 
once  asked,  "  that  the  Crimes  Act  of  1887  did  not 
diminish  disorder  in  Ireland  ? "  But  chronological 
sequence  alone  is  not  a  proof  of  causation  as  long  as 
there  are  other  contemporaneous  changes  of  condition 
that  may  also  have  been  influential. 

The  great  source  of  fallacy  is  our  proneness  to 
eliminate  or  isolate  in  accordance  with  our  prejudices. 
This  has  led  to  the  gibe  that  anything  can  be  proved 
by  statistics.  Undoubtedly  statistics  may  be  made  to 
prove  anything  if  you  have  a  sufficiently  low  standard 
of  proof  and  ignore  the  facts  that  make  against  your 
conclusion.  But  averages  and  variations  in  them  are 
instructive  enough  if  handled  with  due  caution.  The 
remedy  for  rash  conclusions  from  statistics  is  not  no 
statistics,  but  more  of  them  and  a  sound  knowledge  of 
the  conditions  of  reasonable  proof, 

23 


354         Inductive  Logic,  or  the  Logic  of  Science. 

II. — THE  PRESUMPTION  FROM  EXTRA-CASUAL 
COINCIDENCE. 

We  have  seen  that  repeated  coincidence  raises  a 
presumption  of  causal  connexion  between  the  coincid- 
ing events.  If  we  find  two  events  going  repeatedly 
together,  either  abreast  or  in  sequence,  we  infer  that 
the  two  are  somehow  connected  in  the  way  of  causa- 
tion, that  there  is  a  reason  for  the  coincidence  in  the 
manner  of  their  production.  It  may  not  be  that  the 
one  produces  the  other,  or  even  that  their  causes  are 
in  any  way  connected :  but  at  least,  if  they  are  inde- 
pendent one  of  the  other,  both  are  tied  down  to  happen 
at  the  same  place  and  time, — the  coincidence  of  both 
with  time  and  place  is  somehow  fixed. 

But  though  this  is  true  in  the  main,  it  is  not  true 
without  qualification.  We  expect  a  certain  amount  of 
repeated  coincidence  without  supposing  causal  con- 
nexion. If  certain  events  are  repeated  very  often 
within  our  experience,  if  they  have  great  positive 
frequency,  we  may  observe  them  happening  together 
more  than  once  without  concluding  that  the  coincidence 
is  more  than  fortuitous. 

For  example,  if  we  live  in  a  neighbourhood  possessed 
of  many  black  cats,  and  sally  forth  to  our  daily  business 
in  the  morning,  a  misfortune  in  the  course  of  the  day 
might  more  than  once  follow  upon  our  meeting  a 
black  cat  as  we  went  out  without  raising  in  our  minds 
any  presumption  that  the  one  event  was  the  result  of 
the  other. 

Certain  planets  are  above  the  horizon  at  certain 
periods  of  the  year  and  below  the  horizon  at  certain 
other  periods.  All  through  the  year  men  and  women 
are  born  who  afterwards  achieve  distinction  in  various 


Supplementary  Methods  of  Investigation.         355 

walks  of  life,  in  love,  in  war,  in  business,  at  the  bar, 
in  the  pulpit.  We  perceive  a  certain  number  of 
coincidences  between  the  ascendancy  of  certain  planets 
and  the  birth  of  distinguished  individuals  without 
suspecting  that  planetary  inference  was  concerned  in 
their  superiority. 

Marriages  take  place  on  all  days  of  the  year :  the 
sun  shines  on  a  good  many  days  at  the  ordinary  time 
for  such  ceremonies  ;  some  marriages  are  happy,  some 
unhappy ;  but  though  in  the  case  of  many  happy 
marriages  the  sun  has  shone  upon  the  bride,  we  regard 
the  coincidence  as  merely  accidental. 

Men  often  dream  of  calamities  and  often  suffer 
calamities  in  real  life :  we  should  expect  the  coinci- 
dence of  a  dream  of  calamity  followed  by  a  reality  to 
occur  more  than  once  as  a  result  of  chance.  There 
are  thousands  of  men  of  different  nationalities  in 
business  in  London,  and  many  fortunes  are  made  :  we 
should  expect  more  than  one  man  of  any  nationality 
represented  there  to  make  a  fortune  without  arguing 
any  connexion  between  his  nationality  and  his  success. 

We  allow,  then,  for  a  certain  amount  of  repeated 
coincidence  without  presuming  causal  connexion  :  can 
any  rule  be  laid  down  for  determining  the  exact 
amount  ? 

Prof.  Bain  has  formulated  the  following  rule : 
"  Consider  the  positive  frequency  of  the  phenomena 
themselves,  and  how  great  frequency  of  coincidence 
must  follow  from  that,  supposing  there  is  neither  con- 
nexion nor  repugnance.  If  there  be  greater  frequency, 
there  is  connexion  ;  if  less,  repugnance." 

I  do  not  know  that  we  can  go  further  definite  in 
precept.  The  number  of  casual  coincidences  bears  a 
certain  proportion  to  the  positive  frequency  of  the 


356         Inductive  Logic >  or  the  Logic  of  Science. 

coinciding  phenomena  :  that  proportion  is  to  be  deter- 
mined by  common-sense  in  each  case.  It  may  be 
possible,  however,  to  bring  out  more  clearly  the  prin- 
ciple on  which  common-sense  proceeds  in  deciding 
what  chance  will  and  will  not  account  for,  although 
our  exposition  amounts  only  to  making  more  clear 
what  it  is  that  we  mean  by  chance  as  distinguished 
from  assignable  reason.  I  would  suggest  that  in 
deciding  what  chance  will  not  account  for,  we  make 
regressive  application  of  a  principle  which  may  be 
called  the  principle  of  Equal  and  Unequal  Alternatives, 
and  which  may  be  worded  as  follows : — 

Of  a  given  number  of  possible  alternatives,  all  equally 
possible,  one  of  which  is  bound  to  occur  at  a  given 
time,  we  expect  each  to  have  its  turn  an  equal 
number  of  times  in  the  long  run.  If  several  of  the 
alternatives  are  of  the  same  kind,  we  expect  an 
alternative  of  that  kind  to  recur  with  a  frequency 
proportioned  to  their  greater  number.  If  any  of 
the  alternatives  has  an  advantage,  it  will  recur  with 
a  frequency  proportioned  to  the  strength  of  that 
advantage. 

Situations  in  which  alternatives  are  absolutely  equal 
are  rare  in  nature,  but  they  are  artificially  created  for 
games  "  of  chance,"  as  in  tossing  a  coin,  throwing 
dice,  drawing  lots,  shuffling  and  dealing  a  pack  of 
cards.  The  essence  of  all  games  of  chance  is  to  con- 
struct a  number  of  equal  alternatives,  making  them  as 
nearly  equal  as  possible,  and  to  make  no  prearrange- 
ment  which  of  the  number  shall  come  off.  We  then 
say  that  this  is  determined  by  chance.  If  we  ask  why 
we  believe  that  when  we  go  on  bringing  off  one  alter- 
native at  a  time,  each  will  have  its  turn,  part  of 


Supplementary  Methods  of  Investigation.          357 

the  answer  undoubtedly  is  that  given  by  De  Morgan, 
namely,  that  we  know  no  reason  why  one  should  be 
chosen  rather  than  another.  This,  however,  is  probably 
not  the  whole  reason  for  our  belief.  The  rational 
belief  in  the  matter  is  that  it  is  only  in  the  long  run 
or  on  the  average  that  each  of  the  equal  alternatives 
will  have  its  turn,  and  this  is  probably  founded  on  the 
experience  of  actual  trial.  The  mere  equality  of  the 
alternatives,  supposing  them  to  be  perfectly  equal, 
would  justify  us  as  much  in  expecting  that  each  would 
have  its  turn  in  a  single  revolution  of  the  series,  in  one 
complete  cycle  of  the  alternatives.  This,  indeed,  may 
be  described  as  the  natural  and  primitive  expectation 
which  is  corrected  by  experience.  Put  six  balls  in  a 
wicker  bottle,  shake  them  up,  and  roll  one  out :  return 
this  one,  and  repeat  the  operation  :  at  the  end  of  six 
draws  we  might  expect  each  ball  to  have  had  its  turn  of 
being  drawn  if  we  went  merely  on  the  abstract  equality 
of  the  alternatives.  But  experience  shows  us  that  in 
six  successive  draws  the  same  ball  may  come  out 
twice  or  even  three  or  four  times,  although  when 
thousands  of  drawings  are  made  each  comes  out  nearly 
an  equal  number  of  times.  So  in  tossing  a  coin, 
heads  may  turn  up  ten  or  twelve  times  in  succession, 
though  in  thousands  of  tosses  heads  and  tails  are 
nearly  equal.  Runs  of  luck  are  thus  within  the 
rational  doctrine  of  chances  :  it  is  only  in  the  long  run 
that  luck  is  equalised  supposing  that  the  events  are 
pure  matter  of  chance,  that  is,  supposing  the  funda- 
mental alternatives  to  be  equal. 

If  three  out  of  six  balls  are  of  the  same  colour,  we 
expect  a  ball  of  that  colour  to  come  out  three  times  as 
often  as  any  other  colour  on  the  average  of  a  long 
succession  of  tries.  This  illustrates  the  second  clause 


358         Inductive  Logic,  or  the  Logic  of  Science. 

of  our  principle.     The  third  is  illustrated   by  a  loaded 
coin  or  die. 

By  making  regressive  application  of  the  principle 
thus  ascertained  by  experience,  we  often  obtain  a  clue 
to  special  causal  connexion.  We  are  at  least  enabled 
to  isolate  a  problem  for  investigation.  If  we  find  one 
of  a  number  of  alternatives  recurring  more  frequently 
than  the  others,  we  are  entitled  to  presume  that  they 
are  not  equally  possible,  that  there  is  some  inequality 
in  their  conditions. 

The  inequality  may  simply  lie  in  the  greater  possible 
frequency  of  one  of  the  coinciding  events,  as  when 
there  are  three  black  balls  in  a  bottle  of  six.  We 
must  therefore  discount  the  positive  frequency  before 
looking  for  any  other  cause.  Suppose,  for  example, 
we  find  that  the  ascendancy  of  Jupiter  coincides  more 
frequently  with  the  birth  of  men  afterwards  dis- 
tinguished in  business  than  with  the  birth  of  men 
otherwise  distinguished,  say  in  war,  or  at  the  bar,  or 
in  scholarship.  We  are  not  at  liberty  to  conclude 
planetary  influence  till  we  have  compared  the  positive 
frequency  of  the  different  modes  of  distinction. 
The  explanation  of  the  more  frequently  repeated 
coincidence  may  simply  be  that  more  men  altogether 
are  successful  in  business  than  in  war  or  law  or 
scholarship.  If  so,  we  say  that  chance  accounts  for 
the  coincidence,  that  is  to  say,  that  the  coincidence 
casual  as  far  as  planetary  influence  is  concerned 

So  in  epidemics  of  fever,  if  we  find  on  taking  a  long 
average  that  more  cases  occur  in  some  streets  of  a 
town  than  in  others,  we  are  not  warranted  in  conclud- 
ing that  the  cause  lies  in  the  sanitary  conditions  of 
those  streets  or  in  any  special  liability  to  infection 
without  first  taking  into  account  the  number  of  families 


Supplementary  Methods  of  Investigation.         359 

in  the  different  streets.  If  one  street  showed  on  the 
average  ten  times  as  many  cases-  as  another,  the 
coincidence  might  still  be  judged  casual  if  there  were 
ten  times  as  many  families  in  it. 

Apart  from  the  fallacy  of  overlooking  the  positive 
frequency,  certain  other  fallacies  or  liabilities  to  error 
in  applying  this  doctrine  of  chances  may  be  specified. 

1.  We  are  apt,  under  the  influence  of  prepossession 
or  prejudice,  to  remember  certain  coincidences  better 
than  others,  and  so  to  imagine  extra-casual  coincidence 
where  none  exists.     This  bias  works  in  confirming  all 
kinds  of  established  beliefs,  superstitious   and  other, 
beliefs  in  dreams,  omens,  retributions,  telepathic  com- 
munications, and  so  forth.     Many  people  believe  that 
nobody  who  thwarts  them  ever  comes  to  good,  and  can 
produce  numerous  instances  from  experience  in  sup- 
port of  this  belief. 

2.  We  are  apt,  after  proving  that  there  is  a  residuum 
beyond  what  chance  will  account  for  on  due  allowance 
made  for  positive  frequency,  to  take  for  granted  that  we 
have  proved  some  particular  cause  for  this  residuum. 
Now  we  have  not  really  explained  the  residuum  by  the 
application  of  the  principle  of  chances :  we  have  only 
isolated  a    problem   for  explanation.     There  may  be 
more  than  chance  will  account  for  :  yet  the  cause  may 
not  be  the  cause  that  we  assign  off-hand.     Take,  for 
example,    the    coincidence   that    has   been    remarked 
between    race   and  different  forms  of  Christianity  in 
Europe.     If  the  distribution  of  religious  systems  were 
entirely  independent  of  race,  it  might  be  said  that  you 
would  expect  one  system  to  coincide  equally  often  with 
different  races   in  proportion  to  the  positive  number 
of  their  communities.     But  the  Greek  system  is  found 
almost   solely  among    Slavonic    peoples,   the  Roman 


360         Inductive  Logic,  or  the  Logic  of  Science. 

among  Celtic,  and  the  Protestant  among  Teutonic. 
The  coincidence  is  greater  than  chance  will  account 
for.  Is  the  explanation  then  to  be  found  in  some 
special  adaptability  of  the  religious  system  to  the 
character  of  the  people  ?  This  may  be  the  right 
explanation,  but  we  have  not  proved  it  by  merely  dis- 
counting chance.  To  prove  this  we  must  show  that 
there  was  no  other  cause  at  work,  that  character  was 
the  only  operative  condition  in  the  choice  of  system, 
that  political  combinations,  for  example,  had  nothing 
to  do  with  it.  The  presumption  from  extra-casual 
coincidence  is  only  that  there  is  a  special  cause :  in 
determining  what  that  is  we  must  conform  to  the 
ordinary  conditions  of  explanation. 

So  coincidence  between  membership  of  the  Govern- 
ment and  a  classical  education  may  be  greater  than 
chance  would  account  for,  and  yet  the  circumstance  of 
having  been  taught  Latin  and  Greek  at  school  may 
have  had  no  special  influence  in  qualifying  the  members 
for  their  duties.  The  proportion  of  classically  educated 
in  the  Government  may  be  greater  than  the  proportion 
of  them  in  the  House  of  Commons,  and  yet  their 
eminence  may  be  in  no  way  due  to  their  education. 
Men  of  a  certain  social  position  have  an  advantage 
in  the  competition  for  office,  and  all  those  men  have 
been  taught  Latin  and  Greek  as  a  matter  of  course. 
Technically  speaking,  the  coinciding  phenomena  may 
be  independent  effects  of  the  same  cause. 

3.  Where  the  alternative  possibilities  are  very 
numerous,  we  are  apt  not  to  make  due  allowance  for 
the  number,  sometimes  overrating  it,  sometimes  under- 
rating it. 

The  fallacy  of  underrating  the  number  is  often  seen 
in  games  of  chance,  where  the  object  is  to  create  a  vast 


Supplementary  Methods  of  Investigation.         361 

number  of  alternatives,  all  equally  possible,  equally 
open  to  the  player,  without  his  being  able  to  affect 
the  advent  of  one  more  than  another.  In  whist,  for 
example,  there  are  some  six  billions  of  possible  hands. 
Yet  it  is  a  common  impression  that,  one  night  with 
another,  in  the  course  of  a  year,  a  player  will  have 
dealt  to  him  about  an  equal  number  of  good  and  bad 
hands.  This  is  a  fallacy.  A  very  much  longer  time 
is  required  to  exhaust  the  possible  combinations. 
Suppose  a  player  to  have  2000  hands  in  the  course  of 
a  year :  this  is  only  one  "  set,"  one  combination,  out 
of  thousands  of  millions  of  such  sets  possible.  Among 
those  millions  of  sets,  if  there  is  nothing  but  chance 
in  the  matter,  there  ought  to  be  all  proportions  of  good 
and  bad,  some  sets  all  good,  some  all  bad,  as  well  as 
some  equally  divided  between  good  and  bad.1 

Sometimes,  however,  the  number  of  possible  alter- 
natives is  overrated.  Thus,  visitors  to  London  often 
remark  that  they  never  go  there  without  meeting  some- 
body from  their  own  locality,  and  they  are  surprised 
at  this  as  if  they  had  the  same  chance  of  meeting  their 
fellow-visitors  and  any  other  of  the  four  millions  of 
the  metropolis.  But  really  the  possible  alternatives 
of  rencounter  are  far  less  numerous.  The  places 
frequented  by  visitors  to  London  are  filled  by  much 
more  limited  numbers :  the  possible  rencounters  are 
to  be  counted  by  thousands  rather  than  by  millions. 

1  See  De  Morgan's  Essay  on  Probabilities,  c.  vi.,  "  On  Common 
Notions  of  Probabilicy  ". 


CHAPTER  IX. 

PROBABLE  INFERENCE  TO  PARTICULARS  —THE 
MEASUREMENT  OF  PROBABILITY. 

UNDOUBTEDLY  there  are  degrees  of  probability.  Not 
only  do  we  expect  some  events  with  more  confidence 
than  others :  we  may  do  so,  and  our  confidence  may 
be  misplaced  :  but  we  have  reason  to  expect  some 
with  more  confidence  than  others.  There  are  different 
degrees  of  rational  expectation.  Can  those  degrees  be 
measured  numerically? 

The  question  has  come  into  Logic  from  the  mathe- 
maticians. The  calculation  of  Probabilities  is  a 
branch  of  Mathematics.  We  have  seen  how  it  may 
be  applied  to  guide  investigation  by  eliminating  what 
is  due  to  chance,  and  it  has  been  vaguely  conceived  by 
logicians  that  what  is  called  the  calculus  of  proba- 
bilities might  be  found  useful  also  in  determining  by 
exact  numerical  measurement  the  probability  of  single 
events.  Dr.  Venn,  who  has  written  a  separate  treatise 
on  the  Logic  of  Chance,  mentions  "accurate  quanti- 
tative apportionment  of  our  belief"  as  one  of  the  goals 
which  Logic  should  strive  to  attain.  The  following 
passage  will  show  his  drift.1 

A  man  in  good  health  would  doubtless  like  to  know 
whether  he  will  be  alive  this  time  next  year.  The  fact 

1  Empirical  Logic,  p.  556. 
(362) 


Probable  Inference  to  Particulars.  363 

will  be  settled  one  way  or  the  other  in  due  time,  if  he  can 
afford  to  wait,  but  if  he  wants  a  present- decision,  Statistics 
and  the  Theory  of  Probability  can  alone  give  him  any 
information.  He  learns  that  the  odds  are,  say  five  to 
one  that  he  will  survive,  and  this  is  an  answer  to  his 
question  as  far  as  any  answer  can  be  given.  Statisticians 
are  gradually  accumulating  a  vast  mass  of  data  of  this 
general  character.  What  they  may  be  said  to  aim  at  is  to 
place  us  in  the  position  of  being  able  to  say,  in  any  given 
time  or  place,  what  are  the  odds  for  or  against  any  at 
present  indeterminable  fact  which  belongs  to  a  class 
admitting  of  statistical  treatment. 

Again,  outside  the  regions  of  statistics  proper — which 
deal,  broadly  speaking,  with  events  which  can  be  numbered 
or  measured,  and  which  occur  with  some  frequency — there 
is  still  a  large  field  as  to  which  some  better  approach 
to  a  reasoned  intensity  of  belief  can  be  acquired.  What 
will  be  the  issue  of  a  coming  war  ?  Which  party  will  win 
in  the  next  election  ?  Will  a  patient  in  the  crisis  of  a 
given  disease  recover  or  not  ?  That  statistics  are  lying 
here  in  the  background,  and  are  thus  indirectly  efficient 
in  producing  and  graduating  our  belief,  I  fully  hold;  but 
there  is  such  a  large  intermediate  process  of  estimating, 
and  such  scope  for  the  exercise  of  a  practised  judgment, 
that  no  direct  appeal  to  statistics  in  the  common  sense 
can  directly  help  us.  In  sketching  out  therefore  the 
claims  of  an  Ideal  condition  of  knowledge,  we  ought 
clearly  to  include  a  due  apportionment  of  belief  to  every 
event  of  such  a  class  as  this.  It  is  an  obvious  defect  that 
one  man  should  regard  as  almost  certain  what  another 
man  regards  as  almost  impossible.  Short,  therefore,  of 
certain  prevision  of  the  future,  we  want  complete  agree- 
ment as  to  the  degree  of  probability  of  every  future  event : 
and  for  that  matter  of  every  past  event  as  well. 

Technically  speaking,  if  we  extend  the  name 
Modality  (see  p.  78)  to  any  qualification  of  the  cer- 
tainty of  a  statement  of  belief,  what  Dr.  Venn  here 


364         Inductive  Logic,  or  the  Logic  of  Science. 

desiderates,  as  he  has  himself  suggested,  is  a  more 
exact  measurement  of  the  Modality  of  propositions. 
We  speak  of  things  as  being  certain,  possible,  impos- 
sible, probable,  extremely  probable,  faintly  probable, 
and  so  forth  :  taking  certainty  as  the  highest  degree  of 
probability1  shading  gradually  down  to  the  zero  of  the 
impossible,  can  we  obtain  an  exact  numerical  measure 
for  the  gradations  of  assurance  ? 

To  examine  the  principles  of  all  the  cases  in  which 
chances  for  and  against  an  occurrence  have  been  cal- 
culated from  real  or  hypothetical  data,  would  be  to 
trespass  into  the  province  of  Mathematics,  but  a  few 
simple  cases  will  serve  to  show  what  it  is  that  the 
calculus  attempts  to  measure,  and  what  is  the  practical 
value  of  the  measurement  as  applied  to  the  probability 
of  a  single  event. 

Suppose  there  are  100  balls  in  a  box,  30  white  and 
70  black,  all  being  alike  except  in  respect  of  colour,  we 
say  that  the  chances  of  drawing  a  black  ball  as  against 
a  white  are  as  7  to  3,  and  the  probability  of  drawing 
black  is  measured  by  the  fraction  ^.  In  believing 
this  we  proceed  on  the  principle  already  explained 
(p.  356)  of  Proportional  Chances.  We  do  not  know 
for  certain  whether  black  or  white  will  emerge,  but 
knowing  the  antecedent  situation  we  expect  black 

1  Mr.  Jevons  held  that  all  inference  is  merely  probable  and  that 
no  inference  is  certain.  But  this  is  a  purposeless  repudiation  of 
common  meaning,  which  he  cannot  himself  consistently  adhere 
to.  We  find  him  saying  that  if  a  penny  is  tossed  into  the  air  it 
will  certainly  come  down  on  one  side  or  the  other,  on  which 
side  being  a  matter  of  probability.  In  common  speech  probability 
is  applied  to  a  degree  of  belief  short  of  certainty,  but  to  say  that 
certainty  is  the  highest  degree  of  probability  does  no  violence  to 
the  common  meaning. 


Probable  Inference  to  Particulars.  365 

rather  than  white  with  a  degree  of  assurance  corres- 
ponding to  the  proportions  of  the  two  in  the  box.  It 
is  our  degree  of  rational  assurance  that  we  measure  by 
this  fraction,  and  the  rationality  of  it  depends  on  the 
objective  condition  of  the  facts,  and  is  the  same  for  all 
men,  however  much  their  actual  degree  of  confidence 
may  vary  with  individual  temperament.  That  black 
will  be  drawn  seven  times  out  of  every  ten  on  an 
average  if  we  go  on  drawing  to  infinity,  is  as  certain 
as  any  empirical  law :  it  is  the  probability  of  a  single 
draw  that  we  measure  by  the  fraction  T7<y. 

When  we  build  expectations  of  single  events  on 
statistics  of  observed  proportions  of  events  of  that 
kind,  it  is  ultimately  on  the  same  principle  that 
rational  expectation  rests.  That  the  proportion  will 
obtain  on  the  average  we  regard  as  certain  :  the  ratio 
of  favourable  cases  to  the  whole  number  of  possible 
alternatives  is  the  measure  of  rational  expectation 
or  probability  in  regard  to  a  particular  occurrence. 
If  every  year  five  per  cent,  of  the  children  of  a  town 
stray  from  their  guardians,  the  probability  of  this  or 
that  child's  going  astray  is  ^  The  ratio  is  a  correct 
measure  only  on  the  assumption  that  the  average  is 
maintained  from  year  to  year. 

Without  going  into  the  combination  of  probabilities, 
we  are  now  in  a  position  to  see  the  practical  value  of 
such  a  calculus  as  applied  to  particular  cases.  There 
has  been  some  misunderstanding  among  logicians  on 
the  point.  Mr.  Jevons  rebuked  Mill  for  speaking  dis- 
respectfully of  the  calculus,  eulogised  it  as  one  of  the 
noblest  creations  of  the  human  intellect,  and  quoted 
Butler's  saying  that  "Probability  is  the  guide  of  life''. 
But  when  Butler  uttered  this  famous  saying  he  was 
probably  not  thinking  of  the  mathematical  calculus  of 


366         Inductive  Logic •,  or  the  Logic  of  Science. 

probabilities  as  applied  to  particular  cases,  and  it  was 
this  special  application  to  which  Mill  attached  com- 
paratively little  value. 

The  truth  is  that  we  seldom   calculate  or  have  any 
occasion  to  calculate  individual  chances  except  as  a 
matter  of  curiosity.      It  is  true  that  insurance  offices 
calculate  probabilities,  but  it  is  not  the  probability  of 
this  or   that   man    dying   at   a   particular  age.     The 
precise  shade  of  probability  for  the  individual,  in  so 
far  as  this  depends  on  vital  statistics,  is  a  matter  of 
indifference  to  the  company  as  long  as  the  average  is 
maintained.     Our   expectations    about  any   individual 
life  cannot  be  measured  by  a  calculation  of  the  chances 
because  a  variety  of  other  elements  affect  those  expec- 
tations.    We  form  beliefs  about  individual  cases,  but 
we  try  to  get  surer  grounds  for  them  than  the  chances 
as  calculable  from  statistical  data.     Suppose  a  person 
were  to  institute  a  home  for  lost  dogs,  he  would  doubt- 
less try  to  ascertain  how  many  dogs  were  likely  to  go 
astray,  and  in  so  doing  would  be  guided  by  statistics. 
But  in  judging  of  the  probability  of  the  straying  of  a 
particular  dog,  he  would  pay  little  heed  to   statistics 
as  determining  the  chances,  but  would  proceed  upon 
empirical  knowledge  of  the  character  of  the  dog  and 
his  master.     Even  in   betting  on  the   field    against   a 
particular   horse,  the    bookmaker   does    not   calculate 
from   numerical  data   such  as   the  number  of  horses 
entered  or  the  number  of  times  the  favourite  has  been 
beaten  :  he  tries  to  get  at  the   pedigree  and  previous 
performances  of  the  various  horses  in   the  running. 
We  proceed  by  calculation  of  chances  only  when  we 
cannot  do  better. 


CHAPTER  X. 
INFERENCE  FROM  ANALOGY. 

THE  word  Analogy  was  appropriated  by  Mill,  in  accor- 
dance with  the  usage  of  the  eighteenth  century,  to 
designate  a  ground  of  inference  distinct  from  that  on 
which  we  proceed  in  extending  a  law,  empirical  or 
scientific,  to  a  new  case.  But  it  is  used  in  various 
other  senses,  more  or  less  similar,  and  in  order  to 
make  clear  the  exact  logical  sense,  it  is  well  to  specify 
some  of  these.  The  original  word  dvoXoyto,  as  em- 
ployed by  Aristotle,  corresponds  to  the  word  Proportion 
in  Arithmetic :  it  signified  an  equality  of  ratios,  10-0x775 
Xdyoov :  two  compared  with  four  is  analogous  to  four 
compared  with  eight.  There  is  something  of  the  same 
meaning  in  the  technical  use  of  the  word  in  Physiology, 
where  it  is  used  to  signify  similarity  of  function  as 
distinguished  from  similarity  of  structure,  which  is 
called  homology  :  thus  the  tail  of  a  whale  is  analogous 
to  the  tail  of  a  fish,  inasmuch  as  it  is  similarly  used 
for  motion,  but  it  is  homologous  with  the  hind  legs  of 
a  quadruped ;  a  man's  arms  are  homologous  with  a 
horse's  fore  legs,  but  they  are  not  analogous  inasmuch 
as  they  are  not  used  for  progression.  Apart  from 
these  technical  employments,  the  word  is  loosely  used 
in  common  speech  for  any  kind  of  resemblance.  Thus 
De  Quincey  speaks  of  the  "analogical"  power  in 
memory,  meaning  thereby  the  power  of  recalling  things 
(367) 


368         Inductive  Logic,  or  the  Logic  of  Science. 

by  their  inherent  likeness  as  distinguished  from  their 
casual  connexions  or  their  order  in  a  series.  But  even 
in  common  speech,  there  is  a  trace  of  the  original 
meaning :  generally  when  we  speak  of  analogy  we 
have  in  our  minds  more  than  one  pair  of  things,  and 
what  we  call  the  analogy  is  some  resemblance  between 
the  different  pairs.  This  is  probably  what  Whately 
had  in  view  when  he  defined  analogy  as  "  resemblance 
of  relations  ". 

In  a  strict  logical  sense,  however,  as  defined  by 
Mill,  sanctioned  by  the  previous  usage  of  Butler  and 
Kant,  analogy  means  more  than  a  resemblance  of 
relations.  It  means  a  preponderating  resemblance 
between  two  things  such  as  to  warrant  us  in  inferring 
that  the  resemblance  extends  further.  This  is  a 
species  of  argument  distinct  from  the  extension  of  an 
empirical  law.  In  the  extension  of  an  empirical  law, 
the  ground  of  inference  is  a  coincidence  frequently 
repeated  within  our  experience,  and  the  inference  is 
that  it  has  occurred  or  will  occur  beyond  that  experi- 
ence :  in  the  argument  from  analogy,  the  ground  of 
inference  is  the  resemblance  between  two  individual 
objects  or  kinds  of  objects  in  a  certain  number  of 
points,  and  the  inference  is  that  they  resemble  one 
another  in  some  other  point,  known  to  belong  to  the 
one,  but  not  known  to  belong  to  the  other.  "  Two 
things  go  together  in  many  cases,  therefore  in  all, 
including  this  one,"  is  the  argument  in  extending  a 
generalisation  :  "  Two  things  agree  in  many  respects, 
therefore  in  this  other,"  is  the  argument  from  analogy. 

The  example  given  by  Reid  in  his  Intellectual  Powers 
has  become  the  standard  illustration  of  the  peculiar 
argument  from  analogy. 

We  may  observe  a  very  great   similitude  between  this 


Inference  from  Analogy.  369 

earth  which  we  inhabit,  and  the  other  planets,  Saturn, 
Jupiter,  Mars,  Venus  and  Mercury.  They  all  revolve  round 
the  sun,  as  the  earth  does,  although  at  different  distances 
and  in  different  periods.  They  borrow  all  their  light  from 
the  sun,  as  the  earth  does.  Several  of  them  are  known  to 
revolve  round  their  axis  like  the  earth,  and  by  that  means 
have  like  succession  of  day  and  night.  Some  of  them  have 
moons,  that  serve  to  give  them  light  in  the  absence  of 
the  sun,  as  our  moon  does  to  us.  They  are  all,  in  their 
motions,  subject  to  the  same  law  of  gravitation  as  the  earth 
is.  From  all  this  similitude  it  is  not  unreasonable  to  think 
that  these  planets  may,  like  our  earth,  be  the  habitation 
of  various  orders  of  living  creatures.  There  is  some  proba- 
bility in  this  conclusion  from  analogy.1 

The  argument  from  analogy  is  sometimes  said  to 
range  through  all  degrees  of  probability  from  certainty 
to  zero.  But  this  is  true  only  if  we  take  the  word 
analogy  in  its  loosest  sense  for  any  kind  of  resemblance. 
If  we  do  this,  we  may  call  any  kind  of  argument  an 
argument  from  analogy,  for  all  inferences  turn  upon 
resemblance.  I  believe  that  if  I  throw  my  pen  in  the 
air  it  will  come  down  again,  because  it  is  like  other 
ponderable  bodies.  But  if  we  use  the  word  in  its 
limited  logical  sense,  the  degree  of  probability  is  much 
nearer  zero  than  certainty.  This  is  apparent  from  the 
conditions  that  logicians  have  formulated  of  a  strict 
argument  from  analogy. 

i.  The  resemblance  must  be  preponderating.  In 
estimating  the  value  of  an  argument  from  analogy,  we 
must  reckon  the  points  of  difference  as  counting  against 
the  conclusion,  and  also  the  points  in  regard  to  which 
we  do  not  know  whether  the  two  objects  agree  or 
differ.  The  numerical  measure  of  value  is  the  ratio  of 

1  Hamilton's  Reid,  p.  236. 
24 


370         Inductive  Logic,  or  the  Logic  of  Science. 

the  points  of  resemblance  to  the  points  of  difference 
plus  the  unknown  points.  Thus,  in  the  argument  that 
the  planets  are  inhabited  because  they  resemble  the 
earth  in  some  respects  and  the  earth  is  inhabited,  the 
force  of  the  analogy  is  weakened  by  the  fact  that  we 
know  very  little  about  the  surface  of  the  planets. 

2.  In  a  numerical  estimate  all  circumstances  that 
hang  together  as  effects  of  one  cause  must  be  reckoned 
as   one.     Otherwise,    we   might   make   a  fallaciously 
imposing  array  of  points  of  resemblance.     Thus  in 
Reid's  enumeration    of  the  agreements  between  the 
earth  and  the  planets,  their  revolution  round  the  sun 
and  their  obedience  to  the  law  of  gravitation   should 
count  as  one  point  of  resemblance.     If  two   objects 
agree  in  a,  b,  c,  d,  e,  but  b  follows  from  a,  and  d  and  e 
from  f,  the  five  points  count  only  as  two. 

3.  If  the  object   to   which   we  infer   is   known    to 
possess  some  property  incompatible  with  the  property 
inferred,  the  general  resemblance  counts  for  nothing. 
The  moon  has  no  atmosphere,  and  we  know  that  air  is 
an  indispensable  condition   of  life.     Hence,  however 
much    the    moon    may   resemble   the   earth,   we  are 
debarred  from  concluding  that  there  are  living  creatures 
on  the  moon   such  as  we  know  to  exist  on  the  earth. 
We  know  also  that  life  such  as  it  is  on  the  earth  is 
possible  only  within  certain  limits  of  temperature,  and 
that  Mercury  is  too  hot  for  life,  and  Saturn  too  cold,  no 
matter  how  great  the  resemblance  to  the  earth  in  other 
respects. 

4.  If  the  property  inferred  is  known  or  presumed  to 
be  a  concomitant  of  one  or   more   of  the --> points   of 
resemblance,  any  argument  from  analogy  is  superfluous. 
This  is,  in  effect,  to  say  that  we  have  no  occasion  to 
argue    from     general    resemblance    when    we    have 


Inference  from  Analogy.  371 

reason  to  believe  that  a  property  follows  from  some- 
thing that  an  object  is  known  to  possess.  If  we  knew 
that  any  one  of  the  planets  possessed  all  the  conditions, 
positive  and  negative,  of  life,  we  should  not  require 
to  reckon  up  all  the  respects  in  which  it  resembles 
the  earth  in  order  to  create  a  presumption  that  it  is 
inhabited.  We  should  be  able  to  draw  the  conclusion 
on  other  grounds  than  those  of  analogy.  Newton's 
famous  inference  that  the  diamond  is  combustible  is 
sometimes  quoted  as  an  argument  from  analogy.  But, 
technically  speaking,  it  was  rather,  as  Professor  Bain 
has  pointed  out,  of  the  nature  of  an  extended  generalisa- 
tion. Comparing  bodies  in  respect  of  their  densities  and 
refracting  powers,  he  observed  that  combustible  bodies 
refract  more  than  others  of  the  same  density ;  and 
observing  the  exceptionally  high  refracting  power  of 
the  diamond,  he  inferred  from  this  that  it  was  com- 
bustible, an  inference  afterwards  confirmed  by  experi- 
ment. "  The  concurrence  of  high  refracting  power 
with  inflammability  was  an  empirical  law  ;  and 
Newton,  perceiving  the  law,  extended  it  to  the  adjacent 
case  of  the  diamond.  The  remark  is  made  by  Brewster 
that  had  Newton  known  the  refractive  powers  of  the 
minerals  greenockite  and  octohedrite,  he  would  have 
extended  the  inference  to  them,  and  would  have  been 
mistaken."  * 

From  these  conditions  it  will  be  seen  that  we  cannot 
conclude  with  any  high  degree  of  probability  from 
analogy  alone.  This  is  not  to  deny,  as  Mr.  Jevons 
seems  to  ruppose,  that  analogies,  in  the  sense  of 
general  reoemblances,  are  often  useful  in  directing 
investigation.  When  we  find  two  things  very  much 
alike,  and  ascertain  that  one  of  them  possesses  a 
1  Bain's  Logic,  ii.  145. 


372         Inductive  Logic,  or  the  Logic  of  Science. 

certain  property,  the  presumption  that  the  other  has 
the  same  is  strong  enough  to  make  it  worth  while 
trying  whether  as  a  matter  of  fact  it  has.  It  is  said 
that  a  general  resemblance  of  the  hills  near  Ballarat 
in  Australia  to  the  Californian  hills  where  gold  had  been 
found  suggested  the  idea  of  digging  for  gold  at  Ballarat. 
This  was  a  lucky  issue  to  an  argument  from  analogy, 
but  doubtless  many  have  dug  for  gold  on  similar 
general  resemblances  without  finding  that  the  resem- 
blance extended  to  that  particular.  Similarly,  many 
of  the  extensions  of  the  Pharmacopeia  have  proceeded 
upon  general  resemblances,  the  fact  that  one  drug 
resembles  another  in  certain  properties  being  a  suffi- 
cient reason  for  trying  whether  the  resemblance  goes 
further.  The  lucky  guesses  of  what  is  known  as 
natural  sagacity  are  often  analogical.  A  man  of  wide 
experience  in  any  subject-matter  such  as  the  weather, 
or  the  conduct  of  men  in  war,  in  business,  or  in 
politics,  may  conclude  to  the  case  in  hand  from  some 
previous  case  that  bears  a  general  resemblance  to  it, 
and  very  often  his  conclusions  may  be  perfectly  sound 
though  he  has  not  made  a  numerical  estimate  of  the 
data. 

The  chief  source  of  fallacy  in  analogical  argument 
is  ignoring  the  number  of  points  of  difference.  It 
often  happens  that  an  amount  of  resemblance  only 
sufficient  for  a  rhetorical  simile  is  made  to  do  duty  as 
a  solid  argument.  Thus  the  resemblance  between  a 
living  body  and  the  body  politic  is  sometimes  used  to 
support  inferences  from  successful  therapeutic  treat- 
ment to  State  policy.  The  advocates  of  annual 
Parliaments  in  the  time  of  the  Commonwealth  based 
their  case  on  the  serpent's  habit  of  annually  casting 
its  skin. 


Inference  from  Analogy.  373 

Wisest  of  beasts  the  serpent  see, 
Just  emblem  of  eternity, 

And  of  a  State's  duration  ; 
Each  year  an  annual  skin  he  takes, 
And  with  fresh  life  and  vigour  wakes 

At  every  renovation. 

Britain  !  that  serpent  imitate. 

Thy  Commons  House,  that  skin  of  State, 

By  annual  choice  restore  ; 
So  choosing  thou  shalt  live  secure, 
And  freedom  to  thy  sons  inure, 

Till  Time  shall  be  no  more. 


Carlyle's  saying  that  a  ship  could  never  be  taken 
round  Cape  Horn  if  the  crew  were  consulted  every 
time  the  captain  proposed  to  alter  the  course,  if  taken 
seriously  as  an  analogical  argument  against  Represen- 
tative Government,  is  open  to  the  objection  that  the 
differences  between  a  ship  and  a  State  are  too  great 
for  any  argument  from  the  one  to  the  other  to  be  of 
value.  It  was  such  fallacious  analogies  as  these  that 
Heine  had  in  view  in  his  humorous  prayer,  "  Heaven 
defend  us  from  the  Evil  One  and  from  metaphors  ". 


THE  UNIVERSITY  SERIES 

A   NEW   SERIES   OF 
USEFUL    AND    IMPORTANT    BOOKS 

EDITED   BY   PROFESSOR   WM.    KNIGHT 


CHARLES   SCRIBNER'S   SONS,    Publishers 


'"THIS  Series,  published  by  John  Murray  in  Eng- 
land and  Charles  Scribner's  Sons  in  America, 
is  designed  to  supply  the  need  so  widely  felt  of 
authorized  books  for  study  and  reference  both  by 
students  and  by  the  general  public. 

The  aim  of  these  Manuals  is  to  educate  rather 
than  to  inform.  In  their  preparation,  details  have 
been  avoided  except  when  they  illustrate  the  working 
of  general  laws  and  the  development  of  principles  ; 
while  the  historical  evolution  of  both  the  literary 
and  scientific  subjects,  as  well  as  their  philosophical 
significance,  has  been  kept  in  view. 

The  remarkable  success  which  has  attended  the 
Series  has  been  largely  due  to  the  union  of  scien- 
tific with  popular  treatment,  and  of  simplicity  with 
thoroughness;  qualities  that  win  the  general  reader 
everywhere,  and  that  in  America  make  several  of 
the  Manuals  highly  useful  as  text-books. 


THE   UNIVERSITY   SERIES 


OUTLINES   OF   ENGLISH    LITERATURE 

By  WILLIAM  RENTON,  Lecturer  to  the  Scottish  Uni- 
versities. i2mo,  with  Diagrams,  $1.00  net. 
CONTENTS:  First  Period  [600-1600],  pages  9-112:  I.  The 
Old  English  Metric  and  Chronicle  [600-1350],  a.  Anglo- 
Saxon;  b.  Anglo-Norman — II.  The  Renascence  [1350-1500] 
— III.  The  Reformation  [1550-1600] — IV.  The  Romantic 
Drama  [1550-1650].  Second  Period  [1600-1900],  pages 
132-232 — V.  The  Serious  Age  [1600-1700] — VI.  The  Age  of 
Gaiety  [1650-1750] — VII.  The  Sententious  Age  [1700-1800] — 
VIII.  The  Sympathetic  Age  [1800-1900] — Appendix:  Litera- 
ture of  America  [1600-1900] — Index  :  Conspectus  of  British 
and  American  Poetry. 

The  general  arrangement  of  the  book  and  valuable  diagrams  showing 
the  division  of  literature  according  to  ages  and  characteristics  combine  to 
make  this  manual  especially  fitted  to  use  in  the  class-room. 

Criticism  is  supplemented  by  exposition,  with  extracts  to  exhibit  the 
fashion  of  a  period,  or  the  style  of  a  master.  The  number  of  authors 
indicates  the  importance  of  a  period,  and  intrinsic  power  the  importance 
of  an  author.  American  literature  is  considered  as  a  part  of  the  whole, 
but  a  brief  summary  of  its  history  and  general  characteristics  is  also  given. 


THE   PHILOSOPHY   OF  THE   BEAUTIFUL 

By  WILLIAM  KNIGHT,  Professor  of  Philosophy  in  the 

University  of  St.  Andrews.     In  two  parts.     T2mo, 

each  $1.00  net. 

(Part  I.  ITS  HISTORY.)  CONTENTS:  Introductory — Pre- 
historic Origins — Oriental  Art  and  Speculation — The  Phil- 
osophy pf  Greece — The  Neoplatonists — The  Graeco-Roman 
Period — Medievalism — The  Philosophy  of  Germany— of 
France — of  Italy — of  Holland — of  Britain — of  America. 

(Part  II.  ITS  THEORY  AND  ITS  RELATION  TO  THE  ARTS.) 
CONTENTS  :  I.  Prolegomena — II.  The  Nature  of  Beauty — III. 
The  Ideal  and  the  Real — IV.  Inadequate  or  Partial  Theories 
of  Beauty — V.  Suggestions  towards  a  more  Complete  Theory 
of  Beauty — VI.  Art,  Its  Nature  and  Functions — VII.  The 
Correlation  of  the  Arts — VIII.  Poetry,  a.  Definitions  and 
Distinctions  ;  b.  Theories  of  Poetry  ;  c.  A  Suggestion  ;  d.  The 
Origin  of  Poetry — IX.  Music,  a.  Its  Nature  and  Essence  ;  b. 
The  Alliance  of  Music  with  Poetry  and  the  other  Arts  ;  c. 
The  Origin  of  Music — X.  Architecture — XI.  Sculpture— XII. 
Painting — XIII.  Dancing — Appendix  A  :  Russian  Aesthetic 
— Appendix  B  :  Danish  Aesthetic. 


THE    UNIVERSITY    SERIES 


THE   USE   AND   ABUSE   OF   MONEY 
By  Dr.  W.  CUNNINGHAM,  Cambridge.     1 2mo,  $1.00  net. 

A  popular  treatise,  and  the  headings.  Social  Problems,  Practical  Ques- 
tions, and  Personal  Duty,  give  a  broad  view  of  the  scope  of  the  book. 
The  subject  is  Capital  in  its  relation  to  Social  Progress,  and  personal  re- 
sponsibility enters  into  the  questions  raised.  The  volume  contains  a  syl- 
labus of  subjects  and  a  list  of  books  for  reference. 

THE    PHYSIOLOGY  OF  THE  SENSES 

By  JOHN  MCKENDRICK,  Professor  of  Physiology  in 
the  University  of  Glasgow,  and  Dr.  SNODGRASS, 
Physiological  Laboratory,  Glasgow.  127  Illustra- 
tions. i2ino,  340  pages,  $1.50  net. 

The  aim  of  this  book  is  to  give  an  account  of  the  functions  of  the 
organs  of  sense  as  found  in  man  and  the  higher  animals.  Simple  experi- 
ments are  suggested  by  which  any  one  may  test  the  statements  for  him- 
self, and  the  book  has  been  so  written  as  to  be  readily  understood  by 
those  who  have  not  made  physiology  a  special  study.  It  will  be  found  a 
suitable  preparation  for  entering  upon  the  questions  that  underlie  physio- 
logical psychology.  Excellent  illustrations  abound. 


ENGLISH   COLONIZATION   AND  EMPIRE 

By   ALFRED   CALDECOTT,    St.  John's  College,  Cam- 
bridge.    i2mo,  with  Maps  and  Diagrams,  $1.00  net. 

The  diffusion  of  European,  and,  more  particularly,  of  English,  civiliza- 
tion is  the  subject  of  this  book.  The  treatment  of  this  great  theme  covers 
the  origin  and  the  historical,  political,  economical  and  ethnological  develop- 
ment of  the  English  colonies.  There  is  thus  spread  before  the  reader  a 
bird's-eye  view  of  the  colonies,  great  and  small,  from  their  origin  until  the 
present  time,  with  a  summary  of  the  wars  and  other  great  events  which 
have  occurred  in  the  progress  of  this  colonizing  work,  and  with  a  careful 
examination  of  some  of  the  most  important  questions,  economical,  com- 
mercial, and  political,  which  now  affect  the  relation  of  the  colonies  and  the 
parent  nation. 

THE  JACOBEAN   POETS 

By   EDMUND    GOSSE,    Hon.    M.A.,    Trinity   College, 
Cambridge.      i2mo,  $1.00  net. 

This  little  volume  is  an  attempt  to  direct  critical  attention  to  all  that 
was  notable  in  English  poetry  from  1603-1625.  It  is  the  first  book  to  con- 
centrate attention  on  the  poetry  produced  during  the  reign  of  James  I. 
Many  writers  appear  here  for  the  first  time  in  a  book  of  this  nature.  The 
aim  has  been  to  find  unfamiliar  beauties  rather  than  to  reprint  for  the 
thousandth  time  what  is  already  familiar. 


THE    UNIVERSITY    SERIES 


THE   FINE   ARTS 

By  G.  BALDWIN  BROWN,  Professor  of  Fine  Arts  in  the 
University  of  Edinburgh,  izmo,  with  Illustrations, 
$1.00  net. 

CONTENTS  :  Part  I. —  Art  as  the  Expression  of  Popular 
Feelings  and  Ideals  : — The  Beginnings  of  Art — The  Festival 
in  its  Relation  to  the  Form  and  Spirit  of  Classical  Art — 
Mediaeval  Florence  and  her  Painters.  Part  II. — The  Formal 
Conditions  of  Artistic  Expression  : — Some  Elements  of  Effect 
in  the  Arts  of  Form — The  Work  of  Art  as  Significant — The 
Work  of  Art  as  Beautiful.  Part  III.— The  Arts  of  Form  :— 
Architectural  Beauty  in  Relation  to  Construction — The  Con- 
ventions of  Sculpture — Painting  Old  and  New. 

YALE  ART  SCHOOL,  NEW  HAVEN,  CONN. 
MESSRS.  CHARLES  SCRIBNER'S  SONS, 

Gentlemen: — As  a  text-book  for  the  study  of  the  "  Fine  Arts,"  there 
is  nothing  in  the  literature  of  the  subject  that  answers  the  requirements  as 
this  little  book. 

The  originality  of  Professor  Brown's  work  is  apparent.  Out  of  a  wide 
familiarity  with  the  classical  literature  of  the  subject  he  has  sifted  the  essen- 
tial truths.  And  of  the  modern  writers  on  aesthetics  he  knows  and  digests 
everything  from  Winkelmann  to  YVhistler.  But  what  distinguishes  this 
book  from  others  and  gives  it  a  special  value  is  the  treatment  of  the  "  Fine 
Arts"  from  their  technical  side.  This  is  especially  evident  in  his  chapter 
on  painting,  which  contains  many  suggestions  of  value  to  the  young  artist 
and  amateur. 

Respectfully  yours,  JOHN  H.  NIEMEYER. 


THE   LITERATURE   OF   FRANCE 

By  H.   G.  KEENE,   Hon.  M.A.  Oxon.      121110,  $1.00 

net. 

CONTENTS  :  Introduction — The  Age  of  Infancy  (a.  Birth) 
— The  Age  of  Infancy  (b.  Growth) — The  Age  of  Adolescence 
(Sixteenth  Century) — The  Age  of  Glory,  Part  I.  Poetry,  etc. 
—The  Age  of  Glory,  Part  II.  Prose— The  Age  of  Reason, 
Part  I.— The  Age  of  Reason,  Part  II.— The  Age  of  "Nature  " 
— Sources  of  Modern  French  Literary  Art :  Poetry — Sources 
of  Prose  Fiction — Appendix — Index. 

EDWARD  S.  JOYNES,  Professor  of  Modern  Languages,  South  Caro- 
lina College. — "  My  first  impressions  are  fully  confirmed.  The  book  is 
interesting  and  able.  It  would  be  difficult  to  compress  into  equal  com- 
pass a  more  satisfactory  or  suggestive  view  of  so  great  a  subject.  As  an 
introductory  text  for  schools  and  colleges  or  private  readers  I  have  seen 
nothing  so  good.  The  book  deserves,  and  I  hope  will  receive,  a  wide 
welcome." 


THE    UNIVERSITY    SERIES 


THE   REALM    OF   NATURE 

An  Outline  of  Physiography.  By  HUGH  ROBERT 
MILL,  D.Sc.  Edin.;  Fellow  of  the  Royal  Society 
of  Edinburgh  ;  Oxford  Lecturer.  Maps  and  68 
Illustrations.  i2mo,  $1.50  net. 

CONTENTS  :  Story  of  Nature — Substance  of  Nature — 
Power  of  Nature — The  Earth  a  Spinning  Ball — The  Earth  a 
Planet — The  Solar  System  and  Universe — The  Atmosphere 
— Atmospheric  Phenomena — Climates — The  Hydrosphere — 
Bed  of  the  Oceans — Crust  of  the  Earth — Action  of  Water  on 
Land — Record  of  the  Rocks — Continental  Area — Life  and 
Living  Creatures — Man  in  Nature — Appendices — Index. 

Prof.  W.  M.  DAVIS,  of  Harvard. — "An  excellent  book,  clear,  com- 
prehensive, and  remarkably  accurate.  .  .  .  One  who  reaches  a  good 
understanding  of  the  book  may  regard  himself  as  having  made  a  real 
advance  in  his  education  towards  an  appreciation  of  nature." 

Prof.  JAMES  D.  DANA,  Yale. — "  Evidently  prepared  by  one  who  under- 
stood his  subject." 

JOURNAL  OF  EDUCATION.—"  It  should  not  only  be  read,  but  owned  by 
every  teacher." 


THE   ELEMENTS   OF   ETHICS 

An  Introduction  to  Moral  Philosophy.  By  J.  H. 
MUIRHEAD,  M.A.,  Royal  Holloway  College,  Eng- 
land. i2mo,  $1.00  net. 

CONTENTS:  Book  I.  The  Science  of  Ethics  :  Problems  of, 
Can  there  be  a  Science  of,  Scope  of  the  Science — Book  II. 
Moral  Judgment:  Object  of,  Standard  of,  Moral  Law — Book 
III.  Theories  of  the  End  :  As  Pleasure,  as  Self-sacrifice, 
Evolutionary  Hedonism — Book  IV.  The  End  as  Good  :  As 
Common  Good,  Forms  of  the  Good — Book  V.  Moral  Prog- 
ress :  Standard  as  Relative,  as  Progressive,  as  Ideal — Bibli- 
ography. 

THE  ACADEMY,  London. — "  There  is  no  other  introduction  which  can 
be  recommended." 

Prof.  J.  A.  QUARLES,  Washington  and  Lee  University.— "I  am 
pleased  with  Muirhead's  '  Elements  of  Ethics.'  It  seems  fresh,  bright, 
thoughtful,  stimulating.  I  shall  use  it  probably  next  year." 

Prof.  J.  STEARNS,  University  of  Wisconsin. — "  An  admirably  clear 
presentation  and  criticism  of  the  teachings  of  the  chief  schools  of  thought 
upon  the  leading  points  of  ethical  theory." 

Prof.  GEORGE  S.  FULLERTON,  University  of  Penn. — "I  find  the  book 
very  clear,  simple,  and  forcible,  and  I  shall  take  pleasure  in  recommend- 
ing it  to  my  students." 


THE    UNIVERSITY    SERIES 


THE   STUDY   OF   ANIMAL   LIFE 
By  J.  ARTHUR  THOMSON,  M.A.,  F.R.S.E.,  University 
of  Edinburgh.     121110,  Illustrated,  $1.50  net. 

CONTENTS:  Part  I.  THE  EVERYDAY  LIFE  OF  ANIMALS. 
The  Wealth  of  Life— The  Webb  of  Life— The  Struggle- 
Shifts  for  a  Living — Social  Life — Domestic  Life — Industries. 
Part  II.  THE  POWERS  OF  LIFE.  Vitality  —  The  Divided 
Labors  of  the  Body — Instinct.  Part  III.  THE  FORMS  OF 
ANIMAL  LIFE.  Elements  of  Structure — Life  History — Past 
History — The  Simplest  Animals — Backboneless  Animals — 
Backboned  Animals.  Part  IV.  THE  EVOLUTION  OF  ANI- 
MAL LIFE.  Evidences  of  Evolution — Evolution  Theories — 
Habits  and  Surroundings — Heredity.  Appendix  I.  Ani- 
mal Life  and  Ours.  Appendix  II.  "Best  Books "  on  Ani- 
mal Life. 

Prof.  J.  H.  COMSTOCK,  Leland  Stanford,  Junior,  University.—'1 1  have 
read  it  with  great  delight.  It  is  an  admirable  work,  giving  a  true  view  of 
the  existing  state  and  tendencies  of  zoology ;  and  it  possesses  the  rare 
merit  of  being  an  elementary  work,  written  from  the  standpoint  of  the 
most  advanced  thought,  and  in  a  manner  to  be  understood  by  the  begin- 
ning student." 

THE   FRENCH   REVOLUTION 
By   CHARLES   E.    MALLET,   Balliol  College,   Oxford. 
1 2  mo,  $1.00  net. 

This  book  has  a  special  value  to  students  and  readers  who  do  not  own 
the  great  works  of  such  writers  as  De  Tocqueville,  Taine,  Michelet,  and 
Von  Sybel.  Mr.  Mallet  presents  economic  and  political  aspects  of  society 
before  the  Revolution  •  attempts  to  explain  why  the  Revolution  came  ;  why 
the  men  who  made  it  failed  to  attain  the  liberty  they  so  ardently  desired,  or 
to  found  the  new  order  which  they  hoped  to  see  in  France ;  by  what  arts 
and  accidents,  owing  to  what  deeper  causes,  an  inconspicuous  minority 
gradually  grew  into  a  victorious  party  ;  how  external  circumstances  kept 
the  revolutionary  fever  up,  and  forced  the  Revolution  forward.  History 
offers  no  problem  of  more  surpassing  interest  and  none  more  perplexing 
or  obscure. 

GREECE  IN  THE  AGE  OF  PERICLES 
By  ARTHUR  J.  GRANT  of  King's  College,  Cam- 
bridge. i2mo,  with  Illustrations,  $1.25  net. 
CONTENTS  :  I.  The  Essentials  of  Greek  Civilization — II. 
The  Religion  of  the  Greeks — III.  Sparta — IV.  The  Earlier 
History  of  Athens — V.  The  Rivalry  of  Athens  and  Sparta — 
VI.  Civil  Wars  in  Greece — VII.  The  Athenian  Democracy — 
VIII.  Pericles  :  His  Policy  and  his  Friends — IX.  Society  in 
Greece — X.  The  Peloponnesian  War  to  the  Death  of  Peri- 
cles— XI.  The  Peloponnesian  War — XII.  .Thought  and  Art 
in  Athens. 


THE    UNIVERSITY    SERIES 


THE   EARTH'S   HISTORY 

An  Introduction  to  Modern  Geology.  By  R.  D. 
ROBERTS,  M.A.,  Camb.,  D.Sc.  Lond.  With  col- 
ored Maps  and  Illustrations.  i2mo,  $1.50  net. 

A  sketch  of  the  methods  and  the  results  of  geological  inquiry  to  help 
those  who  wish  to  take  up  the  study  in  its  most  interesting  features.  The 
purpose  is  to  answer  such  questions  as  readily  suggest  themselves  to  the 
student,  among  which  may  be  mentioned  the  following :  What  is  the  nature 
of  the  crust  movements  to  which  the  land-areas  and  mountain  ranges  are 
due?  What  was  the  distribution  of  land  and  water  that  obtained  in  the 
area  when  each  group  of  rocks  was  formed  ?  What  was  the  condition  of  its 
surface,  and  what  the  forms  of  life  inhabiting  it  ?  What  were  the  oceanic 
conditions ;  the  depths  in  different  parts  ;  the  forms  of  life  inhabiting  the 
water ;  and  the  nature  and  extent  of  the  materials  brought  down  by  the 
rivers  that  poured  into  the  seas  from  the  land-areas  of  the  period  ? 

UNIVERSITY  EXTENSION  WORLD. — "  Well  adapted  to  the  use  of  classes 
in  the  higher  grades  of  high  schools  and  academies." 

SCIENCE.— "A  useful  compend  to  all  who  desire  knowledge  of  the 
principles  without  having  to  wade  through  a  mass  of  details." 


LOGIC,   INDUCTIVE   AND   DEDUCTIVE 

By  WILLIAM  MINTO,  M.A.,  Hon.  LL.D.,  St.  An- 
drews, Late  Professor  of  Logic'  in  the  University 
of  Aberdeen.  With  Diagrams.  385  pages.  12010, 
$1.25  net. 

FROM  THE  PREFACE.—"  In  this  little  treatise  two  things  are 
attempted.  One  of  them  is  to  put  the  study  of  logical  formula;  on  a 
historical  basis.  The  other,  which  might  at  first  appear  inconsistent 
with  this,  is  to  increase  the  power  of  Logic  as  a  practical  discipline. 
The  main  purpose  of  this  practical  science,  or  scientific  art,  is  con- 
ceived to  be  the  organization  of  reason  against  error,  and  error  in  its 
various  kinds  is  made  the  basis  of  the  division  of  the  subject.  To  carry 
out  this  practical  aim  along  with  the  historical  one  is  not  hopeless, 
because  throughout  its  long  history  Logic  has  been  a  practical  science; 
and,  as  I  have  tried  to  show  at  some  length  in  introductory  chapters, 
has  concerned  itself  at  different  periods  with  the  risks  of  error  peculiar 
to  each." 

Prof.  G.  H.  PALMER,  of  Harvard. — "  It  is  a  charming  book,  inapt 
as  the  adjective  would  ordinarily  seem  for  describing  a  logical  treatise. 
Rarely  does  one  find  within  so  short  a  compass  such  ample  learning,  lucid 
arrangement,  captivating  style,  subservience  to  readers'  needs.  Every  page 
is  stamped  with  the  individuality  of  the  writer  and  with  the  reality  of  the 
subject  with  which  he  deals." 

Prof.  G.  M.  DUNCAN,  of  Yale.— "When  one  reads  for  recreation  in 
the  intervals  between  college  examinations  in  the  hot  days  of  June  a  work 
on  logic,  the  work  must  possess  merits  of  a  high  order.  I  have  been  thus 
reading  Professor  Minto's  book.  It  is  the  best  manual  that  has  appeared 
since  Jevons  published  his  Lessons.  I  shall  recommend  it  to  my  students 
in  the  autumn." 


THE    UNIVERSITY    SERIES 


CHAPTERS   IN   MODERN   BOTANY 

By  PATRICK  GEDDES,  Professor  of  Botany,  Univers- 
ity College,  Dundee.     12010,  Illustrated,  $1.25  net. 

Beginning  with  some  of  the  strangest  forms  and  processes  of  the 
vegetable  world  (Pitcher  Plants),  it  exhibits  these,  not  merely  as  a  vege- 
table menagerie,  but  to  give,  as  speedily  and  interestingly  as  may  be  : 

(a)  Some  general  comprehension  of  the  processes  and  forms  of  vege- 
table life,  and,  from  the  very  first, 

(b)  Some  intelligent  grasp  of  the  experimental  methods  and  reasoning 
employed  in  their  investigation. 

Other  Insectiverous  Plants,  with  their  Movements  and  Nervous  Ac- 
tion, are  discussed.  The  Web  of  Life,  Relations  between  Plants  and 
Animals,  Spring  and  its  Studies,  Geographical  Distribution,  Landscapes, 
Leaves,  etc.,  form  the  subject  of  other  chapters,  all  handled  in  a  way  to 
open  the  general  subject  of  systematic  botany  most  invitingly. 


THE   ENGLISH   NOVEL 

Being  a  Short  Sketch  of  its  History  from  the  Ear- 
liest'Times  to  the  Appearance  of  Waverley.  By 
WALTER  RALEIGH,  Professor  of  Modern  Litera- 
ture at  University  College,  Liverpool.  i2mo, 
$1.25  net. 

CONTENTS  :  I.  The  Romance  and  the  Novel — II.  The 
Elizabethan  Age  :  Euphues — III.  The  Elizabethan  Age  : 
Sidney  and  Nash — IV.  The  Romance  of  the  Seventeenth 
Century — V.  The  Beginnings  of  the  Modern  Novel — VI. 
Richardson  and  Fielding — VII.  The  Novels  of  the  Eighteenth 
Century— VIII.  The  Revival  of  Romance— IX.  The  Novel 
of  Domestic  Satire  :  Miss  Burney,  Miss  Austin,  Miss  Edge- 
worth — X.  Sir  Walter  Scott. 

The  book  furnishes  critical  studies  of  the  work  of  the  chief  English 
novelists  before  Scott,  connected  by  certain  general  lines  of  reasoning  and 
speculation  on  the  nature  and  development  of  the  novel.  Most  of  the 
material  has  been  given  by  the  author  in  the  form  of  lectures  to  his  classes, 
and  possesses  the  merit  of  being  specially  prepared  for  use  in  the  class- 


CHARLES    SCRIBNER'S    SONS 

PUBLISHERS, -IMPORTERS,  AND  BOOKSELLERS 
I53-I57  FIFTH  AVENUE,         -  NEW  YORK  CITY 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 
LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


!»%'<<.,  . 

REC'D  r  n 

~w  *-*    L.O 

MAY     i  >*, 

PI  320 

4  '«$? 

70ct158RH| 

^tv-***1*!  in 

ftCP    0  1    1QiIQ 

PtV  61  1300 

261^'^^ 

•  -     ;    i"^i 

R£C  'U  U-L 

JAN  1  -  ly62 

RECEIVED 

JUM1819W    » 

.nix  W^ftfi  ^  &!K 

JUN12BB-7PW 

LD  21A-50m-8,'57 
(C8481slO)476B 


General  Library 

University  of  California 

Berkeley 


